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148-493: The adjective "NS" reflects the fact that in the RNS formalism , these fields appear in the NS–NS sector in which all vector fermions are anti-periodic. Both uses of the word "NS" refer to André Neveu and John Henry Schwarz , who studied such boundary conditions (the so-called Neveu–Schwarz boundary conditions ) and the fields that satisfy them in 1971. The Kalb–Ramond field generalizes

296-425: A m = e ϕ δ a m {\displaystyle e_{a}^{m}=e^{\phi }\delta _{a}^{m}} and χ a = γ a ξ {\displaystyle \chi _{a}=\gamma _{a}\xi } , where ϕ {\displaystyle \phi } and ξ {\displaystyle \xi } decouple from

444-474: A Bachelor of Science in Engineering (B.S.E.). Typically, A.B. students choose a major (called a concentration) at the end of sophomore year, while B.S.E. students declare at the end of their freshman year. Students must complete distribution requirements, departmental requirements, and independent work to graduate with either degree. A.B. students must complete distribution requirements in literature and

592-430: A Laurent series where O n {\displaystyle {\mathcal {O}}_{n}} are known as the modes and ν = 0 {\displaystyle \nu =0} or 1 / 2 {\displaystyle 1/2} depending on whether the operator is periodic or antiperiodic, respectively. The holomorphic stress-energy tensor and holomorphic supercurrent together form

740-417: A BRST exact state, also called a null state Q B | η ⟩ {\displaystyle Q_{B}|\eta \rangle } , being equivalent | ψ ⟩ ∼ | ψ ⟩ + Q B | η ⟩ {\displaystyle |\psi \rangle \sim |\psi \rangle +Q_{B}|\eta \rangle } . There

888-587: A Collegiate Gothic project), Robert Venturi and Denise Scott Brown ( Frist Campus Center , among several others), Minoru Yamasaki (Robertson Hall), and Rafael Viñoly ( Carl Icahn Laboratory). A group of 20th-century sculptures scattered throughout the campus forms the Putnam Collection of Sculpture. It includes works by Alexander Calder ( Five Disks: One Empty ), Jacob Epstein ( Albert Einstein ), Henry Moore ( Oval with Points ), Isamu Noguchi ( White Sun ), and Pablo Picasso ( Head of

1036-611: A Woman ). Richard Serra 's The Hedgehog and The Fox is located between Peyton and Fine halls next to Princeton Stadium and the Lewis Library. At the southern edge of the campus is Lake Carnegie, an artificial lake named for Andrew Carnegie. Carnegie financed the lake's construction in 1906 at the behest of a friend and his brother who were both Princeton alumni. Carnegie hoped the opportunity to take up rowing would inspire Princeton students to forsake football , which he considered "not gentlemanly." The Shea Rowing Center on

1184-409: A closed algebra known as the N = 1 {\displaystyle N=1} super Virasoro algebra . Using a mode expansion where the stress tensor modes are given by L n {\displaystyle L_{n}} and the supercurrent modes by G r {\displaystyle G_{r}} , the algebra takes the form where c {\displaystyle c}

1332-439: A comprehensive collection of over 20,000 photographs. Approximately 750 works of African art are represented. The Museum oversees the outside John B. Putnam Jr., Memorial Collection of Sculpture . The Princeton University Chapel is located on the north side of campus near Nassau Street. It was built between 1924 and 1928 at a cost of $ 2.3 million, approximately $ 40.8 million adjusted for inflation in 2020. Ralph Adams Cram,

1480-455: A desire to provide direct access to works of art in a museum for a curriculum in the arts, an education system familiar to many European universities at the time. The museum took on the purposes of providing "exposure to original works of art and to teach the history of art through an encyclopedic collection of world art." Numbering over 112,000 objects, the collections range from ancient to contemporary art and come from Europe, Asia, Africa, and

1628-654: A fairly isolated dormitory; a security system was added, although the women deliberately broke it within a day. In 1971, Mary St. John Douglas and Susan Savage Speers became the first female trustees, and in 1974, quotas for men and women were eliminated. Following a 1979 lawsuit, the eating clubs were required to go coeducational in 1991, after an appeal to the U.S. Supreme Court was denied. In 2001, Princeton elected its first female president. The main campus consists of more than 200 buildings on 600 acres (2.4 km ) in Princeton, New Jersey. The James Forrestal Campus,

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1776-408: A frequent occurrence during Green's tenure, enrollment did increase under his administration. In 1823, James Carnahan became president, arriving as an unprepared and timid leader. With the college riven by conflicting views between students, faculty, and trustees, and enrollment hitting its lowest in years, Carnahan considered closing the university. Carnahan's successor, John Maclean Jr. , who

1924-442: A major fundraising drive known as "A Campaign for Princeton" was conducted. President Harold T. Shapiro would succeed Bowen and remain president until 2001. Shapiro would continue to increase the endowment, expand academic programs, raise student diversity, and oversee the most renovations in Princeton's history. One of Shapiro's initiatives was the formation of the multidisciplinary Princeton Environmental Institute in 1994, renamed

2072-493: A model containing only bosons . Shortly after their second paper on this topic, they realized that their model can be combined with Ramond's fermionic model, which they successfully did to give rise to the Ramond–Neveu–Schwarz (RNS) model, referred to at the time as the dual pion model. This work was done with only hadronic physics in mind with no reference to strings, until 1974 when Stanley Mandelstam reinterpreted

2220-634: A number of these sectors can give rise to consistent tachyon-free theories. In particular, the RNS model gives rise to type IIA and type IIB string theory for closed strings, while combining the open string with a modified version of the IIB string gives rise to type I string theory. Starting instead from a ( 1 , 0 ) {\displaystyle (1,0)} supergravity action gives rise to heterotic string theories. One way to classify all possible string theories that can be constructed using this formalism

2368-402: A pair of commutating fields β {\displaystyle \beta } and γ {\displaystyle \gamma } with weight h β = 3 / 2 {\displaystyle h_{\beta }=3/2} and h γ = 1 / 2 {\displaystyle h_{\gamma }=1/2} . These have an action of

2516-456: A part of The New Plan of Study. He also brought about great expansion to the university, with the creation of the School of Architecture in 1919, the School of Engineering in 1921, and the School of Public and International Affairs in 1930. By the end of his presidency, the endowment had increased by 374 percent, the total area of the campus doubled, the faculty experienced impressive growth, and

2664-1443: A physical interpretation as the coordinates of the string worldsheet embedded in spacetime, with μ {\displaystyle \mu } running over the number of spacetime dimensions. For superstring theory in flat spacetime consistency of the theory requires exactly ten dimensions. The partial derivatives are derivatives in complex coordinates ∂ = ∂ z {\displaystyle \partial =\partial _{z}} and ∂ ¯ = ∂ z ¯ {\displaystyle {\bar {\partial }}=\partial _{\bar {z}}} . Operators can be classified according to their behavior under rigid rescaling z ′ = ζ z {\displaystyle z'=\zeta z} . If they transform as O ′ ( z ′ , z ¯ ′ ) = ζ − h ζ ¯ − h ~ O ( z , z ¯ ) {\displaystyle {\mathcal {O}}'(z',{\bar {z}}')=\zeta ^{-h}{\bar {\zeta }}^{-{\tilde {h}}}{\mathcal {O}}(z,{\bar {z}})} they are said to have weight ( h , h ~ ) {\displaystyle (h,{\tilde {h}})} . The weights of

2812-479: A program for servicemen, so they could resume their education once discharged. The post-war years saw scholars renewing broken bonds through numerous conventions, expansion of the campus, and the introduction of distribution requirements. The period saw the desegregation of Princeton, which was stimulated by changes to the New Jersey constitution. Princeton began undertaking a sharper focus towards research in

2960-537: A scholarly conference, a series of short plays, and an art project. In April 2018, university trustees announced that they would name two public spaces for James Collins Johnson and Betsey Stockton , enslaved people who lived and worked on Princeton's campus and whose stories were publicized by the project. In 2019, large-scale student activism again entered the mainstream concerning the school's implementation of federal Title IX policy relating to campus sexual assault . The activism consisted of sit-ins in response to

3108-407: A site for religious services and local celebrations. Measured on the exterior, the chapel is 277 feet (84 m) long, 76 feet (23 m) wide at its transepts , and 121 feet (37 m) high. The exterior is Pennsylvania sandstone , trimmed with Indiana limestone , and the interior is made of limestone and Aquia Creek sandstone . The design evokes characteristics of an English church of

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3256-563: A smaller location designed mainly as a research and instruction complex, is split between nearby Plainsboro and South Brunswick . The campuses are situated about one hour from both New York City and Philadelphia on the train. The university also owns more than 520 acres (2.1 km ) of property in West Windsor Township , and is where Princeton is planning to construct a graduate student housing complex, which will be known as "Lake Campus North". The first building on campus

3404-666: A string interpretation, whereby mesons behave as strings of finite length. In 1970 Pierre Ramond was working at Yale trying to extend the dual resonance models to include fermionic degrees of freedom through a generalization of the Dirac equation . This led him to constructing the first superalgebra , the Ramond superalgebra. At the same time, Andre Neveu and John Schwarz were working at Princeton to extend existing dual resonance models by adding to them anticommutating creation and annihilation operators . This originally gave rise to

3552-602: A student's disciplinary sentence. In April 2024, students joined other campuses across the United States in protests and establishing encampments against the Israel–Hamas war and the alleged genocide of Palestinians in Gaza. The protestors called for divestment from Israel , started a hunger strike and were joined by faculty. The sit-in of Clio Hall led to arrests by police. Activism and protests continued in

3700-772: A university focus on undergraduates. The university has ties with the Institute for Advanced Study, Princeton Theological Seminary , Rutgers University, and the Westminster Choir College of Rider University . Princeton is a member of the Association of American Universities , the Universities Research Association , and the National Association of Independent Colleges and Universities . The university

3848-526: A university in 1896 and was subsequently renamed Princeton University. The university is governed by the Trustees of Princeton University and has an endowment of $ 37.7 billion, the largest endowment per student in the United States. Princeton provides undergraduate and graduate instruction in the humanities , social sciences , natural sciences , and engineering to approximately 8,500 students on its main campus spanning 600 acres (2.4 km ) within

3996-405: Is classified among "R1: Doctoral Universities – Very high research activity" and has one of the largest university libraries in the world. Princeton uses a residential college system and is known for its eating clubs for juniors and seniors. The university has over 500 student organizations. Princeton students embrace a wide variety of traditions from both the past and present. The university

4144-521: Is 3–4 hours a week, although this can vary depending on the course. The student to faculty ratio is 5 to 1, and a majority of classes have fewer than 20 students. In the Fiske Guide to Colleges , academic culture is considered as "tight-knit, extremely hardworking, highly cooperative, and supportive." Undergraduates agree to adhere to an academic integrity policy called the Honor Code. Under

4292-401: Is Christopher Eisgruber, who was appointed by the university's board of trustees in 2013. The board is responsible for the overall direction of the university. It consists of no fewer than 23 and no more than 40 members at any one time, with the president of the university and the governor of New Jersey serving as ex officio members . It approves the operating and capital budgets, supervises

4440-571: Is a stub . You can help Misplaced Pages by expanding it . RNS formalism In string theory , the Ramond–Neveu–Schwarz (RNS) formalism is an approach to formulating superstrings in which the worldsheet has explicit superconformal invariance but spacetime supersymmetry is hidden, in contrast to the Green–Schwarz formalism where the latter is explicit. It was originally developed by Pierre Ramond , André Neveu and John Schwarz in

4588-482: Is accredited by the Middle States Commission on Higher Education (MSCHE), with its last reaffirmation in 2014. Princeton University's endowment of $ 37 billion (per 2021 figures) was ranked as the fourth largest endowment in the United States, and it had the greatest per-student endowment in the world at over $ 4.4 million per student. The endowment is sustained through continued donations and

Kalb–Ramond field - Misplaced Pages Continue

4736-902: Is an NCAA Division I school and competes in the Ivy League. The school's athletic team, the Princeton Tigers , has won the most titles in its conference and has sent many students and alumni to the Olympics . As of October 2021, 75 Nobel laureates , 16 Fields Medalists and 16 Turing Award laureates have been affiliated with Princeton University as alumni, faculty members, or researchers. In addition, Princeton has been associated with 21 National Medal of Science awardees, 5 Abel Prize awardees, 11 National Humanities Medal recipients, 217 Rhodes Scholars , 137 Marshall Scholars , and 62 Gates Cambridge Scholars . Two U.S. presidents , twelve U.S. Supreme Court justices (three of whom serve on

4884-763: Is an accepted version of this page Princeton University is a private Ivy League research university in Princeton, New Jersey , United States. Founded in 1746 in Elizabeth as the College of New Jersey , Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution . The institution moved to Newark in 1747 and then to its Mercer County campus in Princeton nine years later. It officially became

5032-421: Is by looking at the possible residual symmetry algebras that can arise. That is, gauge fixing does not always fully fix the entire gauge symmetry, but can instead leave behind some unfixed residual symmetry whose action keeps the gauge fixed action unchanged. The algebra corresponding to this residual symmetry is known as the constraint algebra . To give rise to a physical theory, this algebra must be imposed on

5180-401: Is formed by acting with r > 0 {\displaystyle r>0} modes at most once on these ground states. The Lorentz covariant , diffeomorphism invariant action for the fermionic superstring is found by coupling the bosonic and fermionic fields to two-dimensional supergravity, giving the action where e a m {\displaystyle e_{a}^{m}}

5328-719: Is formed using a ( 1 , 1 ) {\displaystyle (1,1)} superconformal field theory on the string worldsheet with an action of the form where ψ μ ( z ) {\displaystyle \psi ^{\mu }(z)} and ψ ~ μ ( z ¯ ) {\displaystyle {\tilde {\psi }}^{\mu }({\bar {z}})} are holomorphic and an antiholomorphic anticommutating fermionic fields and X μ ( z , z ¯ ) {\displaystyle X^{\mu }(z,{\bar {z}})} are bosonic fields. These bosonic fields have

5476-548: Is given by that for a string coupled to the Kalb–Ramond field has the form This term in the action implies that the fundamental string of string theory is a source of the NS–NS B -field, much like charged particles are sources of the electromagnetic field. The Kalb–Ramond field appears, together with the metric tensor and dilaton , as a set of massless excitations of a closed string . This string theory -related article

5624-463: Is given by The presence of worldsheet supersymmetry gives rise to worldsheet supercurrents with the holomorphic supercurrent having weight ( 3 / 2 , 0 ) {\displaystyle (3/2,0)} and being given by Any holomorphic operator O ( z ) {\displaystyle {\mathcal {O}}(z)} with weight ( h , 0 ) {\displaystyle (h,0)} can be expanded out as

5772-590: Is inherited from the periodicity of the fermions. For open strings, the boundary condition requires that the surface term in the equations of motion vanishes which imposes the constraints Thus, there are only two sectors for open strings, the R sector and the NS sector. It is often convenient to combine the two fields into a single field with an extended range 0 ≤ σ 1 ≤ 2 π {\displaystyle 0\leq \sigma ^{1}\leq 2\pi } defined according to where now

5920-578: Is known as the Ramond (R) boundary condition and the antiperiodic case ( ν = 1 / 2 {\displaystyle \nu =1/2} ) is known as the Neveu–Schwarz (NS) boundary condition . This gives four possible ways of putting fermions on the closed string, giving rise to four sectors in the Hilbert space, the NS–NS, NS–R, R–NS, and R–R sectors. The periodicity of the supercurrents

6068-512: Is maintained by investment advisers. Princeton's operating budget is over $ 2 billion per year, with 50% going to academic departments and programs, 33% to administrative and student service departments, 10% to financial aid departments, and 7% to the Princeton Plasma Physics Laboratory . Princeton follows a liberal arts curriculum, and offers two bachelor's degrees to students: a Bachelor of Arts (A.B.) and

Kalb–Ramond field - Misplaced Pages Continue

6216-686: Is only acquired if the spectrum of states is restricted through a procedure known as a GSO projection , with this projection being automatically present in the Green–Schwarz formalism. The discovery of the Veneziano amplitude describing the scattering of four mesons in 1968 launched the study of dual resonance models which generalized these scattering amplitudes to the scattering with any number of mesons. While these are S-matrix theories rather than quantum field theories , Yoichiro Nambu , Holger Bech Nielsen , and Leonard Susskind gave them

6364-908: Is only one copy. Closed strings are periodic in their spatial direction, a periodicity that must be respected by the fields living on the worldsheet. A Poincaré invariant theory must have periodic X μ ( σ 1 , σ 2 ) {\displaystyle X^{\mu }(\sigma _{1},\sigma _{2})} . For the fermionic fields, Lorentz invariance allows for two possible boundary condition ; periodic or antiperiodic boundary conditions ψ μ ( σ 1 + 2 π , σ 2 ) = ± ψ μ ( σ 1 , σ 2 ) {\displaystyle \psi ^{\mu }(\sigma _{1}+2\pi ,\sigma _{2})=\pm \psi ^{\mu }(\sigma _{1},\sigma _{2})} , with an analogous condition for

6512-750: Is that type IIA theory only keeps sectors with e i π F = + 1 {\displaystyle e^{i\pi F}=+1} and e i π F ~ = ( − 1 ) α ~ {\displaystyle e^{i\pi {\tilde {F}}}=(-1)^{\tilde {\alpha }}} , while IIB theory only keeps sectors with e i π F = e i π F ~ = + 1 {\displaystyle e^{i\pi F}=e^{i\pi {\tilde {F}}}=+1} . Type I string theory can be constructed from type IIB theory that has gauged its worldsheet parity symmetry and has been combined with

6660-457: Is the central charge . The algebra is sometimes referred to as the Ramond algebra when r {\displaystyle r} , s {\displaystyle s} are integers and the Neveu–Schwarz algebra when they are half-integers. For closed strings there are two copies of this algebra, one for the holomorphic and one for the antiholomorphic side, while for open strings there

6808-504: Is the additional condition that b 0 | ψ ⟩ = L 0 | ψ ⟩ = 0 {\displaystyle b_{0}|\psi \rangle =L_{0}|\psi \rangle =0} , and for the R sector states β 0 | ψ ⟩ = G 0 | ψ ⟩ = 0 {\displaystyle \beta _{0}|\psi \rangle =G_{0}|\psi \rangle =0} . This condition truncates

6956-429: Is the corresponding charge associated with this current The physical spectrum is the set of BRST cohomology classes . This is the set of states | ψ ⟩ {\displaystyle |\psi \rangle } that are annihilated by the charge Q B | ψ ⟩ = 0 {\displaystyle Q_{B}|\psi \rangle =0} , with all states differing by

7104-405: Is the projection of the Hilbert space onto the subset of sectors that are consistent under these three conditions. One set of consistent theories that results from the projection are type 0 string theories , although these are not tachyon-free. The other set of consistent theories are type II string theories which are tachyon-free, consisting of the sectors A concise way to summarize these sectors

7252-430: Is the two-dimensional vielbein and χ a {\displaystyle \chi _{a}} is the corresponding gravitino . This has the following symmetries: The gauge symmetries of this action are diffeomorphism symmetry, Weyl symmetry, and local supersymmetry. To quantize the action, these symmetries must be gauge fixed, which is usually done through the superconformal gauge in which e

7400-462: The SO ( 8 ) {\displaystyle {\text{SO}}(8)} representation, with this being the direct product of the left-moving and right-moving representations, which decomposes into a sum over irreducible representations . There are no states where NS− is matched with NS+, R− or R+ since then the level matching condition is not meet, so the closed string theory has a single tachyon coming from

7548-438: The ( 1 , 1 ) {\displaystyle (1,1)} superconformal algebra, the other allowed algebras are the ( 1 , 0 ) {\displaystyle (1,0)} , ( 1 , 2 ) {\displaystyle (1,2)} and ( 0 , 2 ) {\displaystyle (0,2)} superconformal algebras. The first of these gives rise to heterotic string theories, while

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7696-414: The ( 1 , 1 ) {\displaystyle (1,1)} supergravity action down to the RNS action leaves behind a residual ( 1 , 1 ) {\displaystyle (1,1)} superconformal algebra . Physical conditions such as unitarity and a positive number of spatial dimensions limits the number of admissible constraint algebras. Besides the conformal algebra and

7844-625: The College of William & Mary in Williamsburg, Virginia ; it was also where some of the founders preached. Although their initial request was rejected by the Anglican governor Lewis Morrison , the acting governor after Morrison's death, John Hamilton , granted a charter for the College of New Jersey on October 22, 1746. In 1747, approximately five months after acquiring the charter,

7992-689: The High Meadows Environmental Institute in 2020. In 2001, Princeton shifted the financial aid policy to a system that replaced all loans with grants. That same year, Princeton elected its first female president, Shirley M. Tilghman . Before retiring in 2012, Tilghman expanded financial aid offerings and conducted several major construction projects like the Lewis Center for the Arts and a sixth residential college. Tilghman also lead initiatives for more global programs,

8140-453: The Hilbert space by projecting out unwanted states. Physical states are the ones that are annihilated by the action of this algebra on those states. For example, in bosonic string theory the original diffeomorphism × {\displaystyle \times } Weyl symmetry breaks down to a residual conformal symmetry , giving the conformal algebra whose generator is

8288-671: The Institute for Advanced Study was founded to provide a space for the influx of scientists, such as Albert Einstein . Many Princeton scientists would work on the Manhattan Project during the war, including the entire physics department. During World War II, Princeton offered an accelerated program for students to graduate early before entering the armed forces. Student enrollment fluctuated from month to month, and many faculty were forced to teach unfamiliar subjects. Still, Dodds maintained academic standards and would establish

8436-720: The Rutgers-Princeton Cannon War . A compromise between the presidents of Princeton and Rutgers ended the war and forced the return of the Little Cannon to Princeton. The protruding cannons are occasionally painted scarlet by Rutgers students who continue the traditional dispute. Though art collection at the university dates back to its very founding, the Princeton University Art Museum was not officially established until 1882 by President McCosh. Its establishment arose from

8584-515: The School of Architecture , the School of Engineering and Applied Science , and the School of Public and International Affairs . Additionally, the school's Bendheim Center for Finance provides education for the area of money and finance in lieu of a business school . Princeton did host a Princeton Law School for a short period, before eventually closing in 1852 due to poor income. Princeton's lack of other professional schools can be attributed to

8732-648: The borough of Princeton. It offers postgraduate degrees through the Princeton School of Public and International Affairs , the School of Engineering and Applied Science , the School of Architecture and the Bendheim Center for Finance . The university also manages the Department of Energy's Princeton Plasma Physics Laboratory and is home to the NOAA's Geophysical Fluid Dynamics Laboratory . It

8880-448: The electromagnetic potential but it has two indices instead of one. This difference is related to the fact that the electromagnetic potential is integrated over one-dimensional worldlines of particles to obtain one of its contributions to the action while the Kalb–Ramond field must be integrated over the two-dimensional worldsheet of the string. In particular, while the action for a charged particle moving in an electromagnetic potential

9028-472: The path integral . The last approach starts from the Euclidean partition function where S {\displaystyle S} is the worldsheet action with some gauge symmetry group G {\displaystyle G} that represents an overcounting of the physically distinct configurations of the fields that the action depends on. This overcounting is eliminated by dividing by

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9176-559: The stress-energy tensor T a b {\displaystyle T^{ab}} . The physical states | ψ ⟩ {\displaystyle |\psi \rangle } , | ψ ′ ⟩ {\displaystyle |\psi '\rangle } are then those for which ⟨ ψ | T a b | ψ ′ ⟩ = 0 {\displaystyle \langle \psi |T^{ab}|\psi '\rangle =0} . Similarly, gauge fixing

9324-515: The vacuum state . Since all annihilation modes for the NS sector have r > 0 {\displaystyle r>0} , it follows that its spectrum has a unique vacuum state | 0 ⟩ NS {\displaystyle |0\rangle _{\text{NS}}} that is annihilated by all the modes The r < 0 {\displaystyle r<0} modes act as raising operators, and since they are anticommuting, each one can be acted on at most once, giving

9472-451: The 2008 plan, Princeton has aimed at reducing its carbon dioxide emissions to 1990 levels without the purchase of market offsets and predicts to meet the goal by 2026 (the former goal was by 2020 but COVID-19 requirements delayed this). Princeton released its second Sustainability Action Plan in 2019 on Earth Day with its main goal being reducing campus greenhouse gases to net zero by 2046 as well as other objectives building on those in

9620-734: The 2008 plan. In 2021, the university agreed to divest from thermal coal and tar sand segments of the fossil fuel industry and from companies that are involved in climate disinformation after student protest. Princeton is a member of the Ivy Plus Sustainability Consortium, through which it has committed to best-practice sharing and the ongoing exchange of campus sustainability solutions along with other member institutions. Princeton's Sustainability Action Plan also aims to have zero waste through recycling programs, sustainable purchasing, and behavioral and operational strategies. Princeton's 20th and current president

9768-630: The Americas. The museum's art is divided into ten extensive curatorial areas. There is a collection of Greek and Roman antiquities , including ceramics, marbles, bronzes, and Roman mosaics from faculty excavations in Antioch , as well as other art from the ancient Egyptian, Byzantium , and Islamic worlds. The non-Islamic coins were catalogued by Dorothy B. Waage . Medieval Europe is represented by sculpture, metalwork, and stained glass. The collection of Western European paintings includes examples from

9916-494: The College of New Jersey initially suggested that Nassau Hall be named in recognition of Belcher because of his interest in the institution; the governor vetoed the request. Burr, who would die in 1757, devised a curriculum for the school and enlarged the student body. Following the untimely death of Burr and the college's next three presidents , John Witherspoon became president in 1768 and remained in that post until his death in 1794. With his presidency, Witherspoon focused

10064-501: The GSO projected open RNS string. The open strings must also have Chan–Paton factors belonging to the SO ( 32 ) {\displaystyle {\text{SO}}(32)} gauge group. This last condition arises from a requirement to make the theory non-anomalous . Heterotic string theories can be constructed using this same formalism, except starting with an action different from the RNS action. Princeton University This

10212-484: The Honor Code, faculty do not proctor examinations; instead, the students proctor one another and must report any suspected violation to an Honor Committee made up of undergraduates. The Committee investigates reported violations and holds a hearing if it is warranted. An acquittal at such a hearing results in the destruction of all records of the hearing; a conviction results in the student's suspension or expulsion. Violations pertaining to all other academic work fall under

10360-599: The Middle Ages . The extensive iconography, in stained glass, stonework, and wood carvings, has the common theme of connecting religion and scholarship. Published in 2008, the Sustainability Action Plan was the first formal plan for sustainability enacted by the university. It focused on reducing greenhouse gas emissions, conservation of resources, and research, education, and civic engagement for sustainability through 10 year objectives. Since

10508-431: The NS sector spectrum. The R sector has zero modes ψ 0 μ {\displaystyle \psi _{0}^{\mu }} which map a vacuum state into another vacuum state. Under the rescaling γ μ = 2 − 1 / 2 ψ 0 μ {\displaystyle \gamma ^{\mu }=2^{-1/2}\psi _{0}^{\mu }} ,

10656-525: The NS−NS− sector. The naive RNS string Hilbert space does not give rise to a consistent string theory. There are three conditions that must be satisfied for the theory to be consistent. First, the vertex operators of the theory have to be mutually local, meaning that their OPEs have no branch cuts. Secondly, the OPEs must also closed . Lastly, the one-loop amplitudes must be modular invariant . The GSO projection

10804-559: The Neveu–Schwarz ground states are defined according to BRST quantization of the theory requires the construction of the BRST current where c {\displaystyle c} and γ {\displaystyle \gamma } are the ghosts and T B , F m , g {\displaystyle T_{B,F}^{m,g}} are the matter and ghost stress tensors and supercurrents. The BRST charge Q B {\displaystyle Q_{B}}

10952-432: The R and NS sectors correspond to a periodicity or antiperiodicity condition on this extended field. The Hilbert space of the R sector and NS sector are determined by considering the modes ψ r μ {\displaystyle \psi _{r}^{\mu }} and ψ ~ r μ {\displaystyle {\tilde {\psi }}_{r}^{\mu }} of

11100-406: The RNS action together with a ghost action describing holomorphic and antiholomorphic ghosts that are necessary to eliminate the unphysical temporal excitations of the fields. The physical states of this theory split up into a number of sectors depending on the periodicity condition of the fermionic fields . The full theory is inconsistent and contains an unphysical tachyon, however projecting out

11248-489: The RNS model as a model for spinning strings. Joël Scherk and John Schwartz were the first to suggest that it may describe elementary particles rather than just hadrons when they showed that the spin -2 particle of the model behaves as a graviton . At the time, the main issue with the RNS model was that it contained a tachyon as the lowest energy state . It was only in 1976 with the introduction of GSO projection by Ferdinando Gliozzi , Joël Scherk, and David Olive that

11396-411: The RNS model in 1971, which gives rise to type II string theories and can also give type I string theory . Heterotic string theories can also be acquired through this formalism by using a different worldsheet action. There are various ways to quantize the string within this framework including light-cone quantization , old canonical quantization, and BRST quantization . A consistent string theory

11544-654: The Synod and devised a plan to establish a new college, for they were disappointed with Harvard and Yale 's opposition to the Great Awakening and dissatisfied with the limited instruction at the Log College. They convinced three other Presbyterians to join them and decided on New Jersey as the location for the college, as at the time, there was no institution between Yale College in New Haven, Connecticut , and

11692-623: The Third World Center (now known as the Carl A. Fields Center) was dedicated in 1971. Goheen also oversaw great expansion for the university, with square footage increasing by 80 percentage. Throughout the 1960s and 1970s, Princeton experienced unprecedented activism, with most of it centered on the Vietnam War . While Princeton activism initially remained relatively timid compared to other institutions, protests began to grow with

11840-622: The United States) from June 30, 1783, to November 4, 1783. Since 1911, the front entrance has been flanked by two bronze tigers, a gift of the Princeton Class of 1879, which replaced two lions previously given in 1889. Starting in 1922, commencement has been held on the front lawn of Nassau Hall when there is good weather. In 1966, Nassau Hall was added to the National Register of Historic Places . Nowadays, it houses

11988-759: The action. Performing this gauge fixing through the Faddeev–Popov procedure leaves behind the RNS action and a BRST ghost action S → S RNS + S g {\displaystyle S\rightarrow S_{\text{RNS}}+S_{g}} . There are holomorphic and antiholomorphic ghosts in the gauge fixed superstring action. On the holomorphic side are a pair of anticommutating b {\displaystyle b} and c {\displaystyle c} fields with weight h b = 2 {\displaystyle h_{b}=2} and h c = − 1 {\displaystyle h_{c}=-1} , along with

12136-733: The administration commissioned a report on admitting women. The final report was issued in January 1969, supporting the idea. That same month, Princeton's trustees voted 24–8 in favor of coeducation and began preparing the institution for the transition. The university finished these plans in April 1969 and announced there would be coeducation in September. Ultimately, 101 female freshman and 70 female transfer students enrolled at Princeton in September 1969. Those admitted were housed in Pyne Hall,

12284-595: The anticommutating ghosts fields being periodic, while the commutating ghost fields being periodic in the R sector and antiperiodic in the NS sector. The modes satisfy the (anti)commutation relations { b m , c n } = δ n , − m {\displaystyle \{b_{m},c_{n}\}=\delta _{n,-m}} and [ γ r , β s ] = δ r , − s {\displaystyle [\gamma _{r},\beta _{s}]=\delta _{r,-s}} . The Ramond and

12432-480: The anticommutating relation for these becomes the Dirac algebra , implying that the ground state of the R spectrum forms a representation of this algebra. In ten dimensions this is a Dirac spinor , a 32 dimensional representation which can be reduced down to two Weyl representations 32 = 16 + 16 ′ {\displaystyle {\text{32}}={\text{16}}+{\text{16}}'} distinguished by their chirality . The R sector spectrum

12580-471: The antiholomorphic fields. This can concisely be summarized as where ν {\displaystyle \nu } and ν ~ {\displaystyle {\tilde {\nu }}} are independent of each other and are either 0 {\displaystyle 0} or 1 / 2 {\displaystyle 1/2} . The periodic case ( ν = 0 {\displaystyle \nu =0} )

12728-412: The armed forces, with 151 dying during the war. After the war, enrollment spiked and the trustees established the system of selective admission in 1922. From the 1920s to the 1930s, the student body featured many students from preparatory schools, zero Black students, and dwindling Jewish enrollment because of quotas. Aside from managing Princeton during WWI, Hibben introduced the senior thesis in 1923 as

12876-445: The arts, science and engineering, social analysis, cultural difference, epistemology and cognition, ethical thought and moral values, historical analysis, and quantitative and computational reasoning; they must also have satisfactory ability in a foreign language. Additionally, they must complete two papers of independent work during their junior year—known as the junior papers—and craft a senior thesis to graduate; both revolve around

13024-574: The board of trustees and dissatisfaction with his administration, he was forced to resign in 1902. Following Patton's resignation, Woodrow Wilson , an alumnus and popular professor, was elected the 13th president of the university. Noticing falling academic standards, Wilson orchestrated significant changes to the curriculum, where freshman and sophomores followed a unified curriculum while juniors and seniors concentrated study in one discipline. Ambitious seniors were allowed to undertake independent work, which would eventually shape Princeton's emphasis on

13172-648: The campus R.O.T.C. chapter in a game of touch football . As the years went on, the protests' agenda broadened to investments in South Africa, environmental issues, and women's rights. In response to these broadening protests, the Council of the Princeton University Community (CPUC) was founded to serve as a method for greater student voice in governance. Activism culminated in 1970 with a student, faculty, and staff member strike , so

13320-494: The cannon was returned to Princeton and placed at the eastern end of town. Two years later, it was moved to the campus under cover of night by Princeton students, and in 1840, it was buried in its current location. A second "Little Cannon" is buried in the lawn in front of nearby Whig Hall. The cannon, which may also have been captured in the Battle of Princeton, was stolen by students of Rutgers University in 1875. The theft ignited

13468-403: The certificates effectively serve as one. Course structure is determined by the instructor and department. Classes vary in their format, ranging from small seminars to medium-sized lecture courses to large lecture courses. The latter two typically have precepts , which are extra weekly discussion sessions that are led by either the professor or a graduate student. The average class meeting time

13616-592: The college became the site for the Battle of Princeton . During the battle, British soldiers briefly occupied Nassau Hall before eventually surrendering to American forces led by General George Washington . During the summer and fall of 1783, the Continental Congress and Washington met in Nassau Hall, making Princeton the country's capital for four months; Nassau Hall is where Congress learned of

13764-473: The college on preparing a new generation of both educated clergy and secular leadership in the new American nation. To this end, he tightened academic standards, broadened the curriculum, solicited investment for the college, and grew its size. A signatory of the Declaration of Independence , Witherspoon and his leadership led the college to becoming influential to the American Revolution . In 1777,

13912-473: The college's president in 1868, and lifted the institution out of a low period that had been brought about by the war. During his two decades of service, he overhauled the curriculum, oversaw an expansion of inquiry into the sciences, recruited distinguished faculty, and supervised the addition of a number of buildings in the High Victorian Gothic style to the campus. McCosh's tenure also saw

14060-628: The concentration they are pursuing. B.S.E. majors complete fewer courses in the humanities and social sciences and instead fulfill requirements in mathematics, physics, chemistry, and computer programming. They likewise must complete independent work, which typically involves a design project or senior thesis, but not the junior papers. A.B. majors must complete 31 courses, whereas B.S.E. majors must complete 36 courses. Students can choose from either 36 concentrations or create their own. They can also participate in 55 interdisciplinary certificate programs; since Princeton does not offer an academic minor ,

14208-460: The construction of two new buildings. In 1807, a large student riot occurred at Nassau Hall, spurred by underlying distrust of educational reforms by Smith away from the Church. Following Smith's mishandling of the situation, falling enrollment, and faculty resignations, the trustees of the university offered resignation to Smith, which he accepted. In 1812, Ashbel Green was unanimously elected by

14356-402: The coordinates ( z , z ¯ ) {\displaystyle (z,{\bar {z}})} defined by z = e − i w {\displaystyle z=e^{-iw}} . For the latter, a string at a given point in time is a circle around the origin in the complex plane , with smaller radii corresponding to earlier times. The RNS model

14504-470: The court as of 2010 ) and numerous living industry and media tycoons and foreign heads of state are all counted among Princeton's alumni body. Princeton has graduated many members of the U.S. Congress and the U.S. Cabinet , including eight secretaries of state , three secretaries of defense and two chairmen of the Joint Chiefs of Staff . Princeton University, founded as the College of New Jersey,

14652-589: The creation and rise of many extracurricular activities, like the Princeton Glee Club , the Triangle Club , the first intercollegiate football team, and the first permanent eating club , as well as the elimination of fraternities and sororities. In 1879, Princeton conferred its first doctorates on James F. Williamson and William Libby, both members of the Class of 1877. Francis Patton took

14800-454: The creation of an office of sustainability, and investments into the sciences. Princeton's 20th and current president, Christopher Eisgruber , was elected in 2013. In 2017, Princeton University unveiled a large-scale public history and digital humanities investigation into its historical involvement with slavery called the Princeton & Slavery Project. The project saw the publication of hundreds of primary sources, 80 scholarly essays,

14948-662: The early Renaissance through the 19th century, with pieces by Monet , Cézanne , and Van Gogh , and features a growing collection of 20th-century and contemporary art, including paintings such as Andy Warhol 's Blue Marilyn. The museum features a collection of Chinese and Japanese art, with holdings in bronzes, tomb figurines, painting, and calligraphy , as well as collections of Korean, Southeast, and Central Asian art. Its collection of pre-Columbian art includes examples of Mayan and Olmec art, and its indigenous art ranges from Chile to Alaska to Greenland. The museum has collections of old master prints and drawings, and it has

15096-603: The end of the 19th century, much of Princeton's architecture was designed by the Cope and Stewardson firm (led by the same University of Pennsylvania professors of architecture who designed a large part of Washington University in St. Louis and University of Pennsylvania ) resulting in the Collegiate Gothic style for which Princeton is known for today. Implemented initially by William Appleton Potter , and later enforced by

15244-648: The enrollment doubled. Hibben's successor, Harold Willis Dodds would lead the university through the Great Depression , World War II , and the Korean Conflict . With the Great Depression, many students were forced to withdraw due to financial reasons. At the same time, Princeton's reputation in physics and mathematics surged as many European scientists left for the United States due to uneasy tension caused by Nazi Germany . In 1930,

15392-461: The fermionic fields. Since in the R sector the powers r {\displaystyle r} are integers, this sector has a branch cut while the NS sector has half-integer r {\displaystyle r} and so no branch cut. The operator product expansion (OPE) of the fermionic theory translate to anticommutation relations for the modes given by The states in the Hilbert space can then be built up by acting with these modes on

15540-430: The first consistent tachyon-free string theories were constructed. The RNS formalism is an approach to quantizing a string by working with the string worldsheet embedded in spacetime with both bosonic and fermionic fields on the worldsheet. There are a number of different approaches for quantizing the string in this formalism. The main ones are old covariant quantization, light-cone quantization, and BRST quantization via

15688-507: The first half of the 20th century. Due to the tightening of academic standards, enrollment declined severely until 1907. In 1906, the reservoir Lake Carnegie was created by Andrew Carnegie , and the university officially became nonsectarian . Before leaving office, Wilson strengthened the science program to focus on "pure" research and broke the Presbyterian lock on the board of trustees. However, he did fail in winning support for

15836-486: The following year in the Graduate School. In 1964, T'sai-ying Cheng became the first woman at Princeton to receive a Ph.D. In 1963, five women came to Princeton for one year to study "critical languages" as undergraduates, but were not candidates for a Princeton degree. Following abortive discussions with Sarah Lawrence College to relocate the women's college to Princeton and merge it with the university in 1967,

15984-406: The form with a similar action for the antiholomorphic ghosts. This action gives rise to additional ghost contributions to the overall stress energy tensor T B g {\displaystyle T_{B}^{g}} and supercurrents of the theory T F g {\displaystyle T_{F}^{g}} . The ghost mode expansion is determined by their weights, with

16132-639: The founding of a local chapter of Students for a Democratic Society (SDS) in 1965, which organized many of the later Princeton protests. In 1966, the SDS gained prominence on campus following picketing against a speech by President Lyndon B. Johnson , which gained frontpage coverage by the New York Times. A notable point of contention on campus was the Institute for Defense Analyses (IDA) and would feature multiple protests, some of which required police action. In 1967, SDS members and sympathizers beat

16280-410: The future as special cases, but does not plan to make general admissions of women graduate students." The student-run Daily Princetonian ran four articles about Meservey in one issue, including an editorial lamenting the potential "far reaching implications" of Meservey's admission which concluded: "Princeton is unique as an undergraduate men's college and must remain so." Eight more women enrolled

16428-449: The ghost spectrum for kinematic reasons. It is convenient to look at the lowest energy states of this theory. Introducing the fermion number operator F {\displaystyle F} allows for the NS and R sectors to be further subdivided into NS−, NS+, R−, and R+ sectors, where the sign denotes the sign of e i π F = ± 1 {\displaystyle e^{i\pi F}=\pm 1} for

16576-494: The honor system was established, allowing for unproctored exams. In 1896, the college officially became a university, and as a result, it officially changed its name to Princeton University. In 1900, the Graduate School was formally established. Even with such accomplishments, Patton's administration remained lackluster with its administrative structure and towards its educational standards. Due to profile changes in

16724-474: The investment of the university's endowment, and oversees campus real estate and long-range physical planning. The trustees also exercise prior review and approval concerning changes in major policies such as those in instructional programs and admission as well as tuition and fees and the hiring of faculty members. The university is composed of the Undergraduate College, the Graduate School ,

16872-505: The jurisdiction of the Faculty-Student Committee on Discipline. Undergraduates are expected to sign a pledge on their written work affirming that they have not plagiarized the work. The first focus on issues of grade inflation by the Princeton administration began in 1998 when a university report was released showcasing a steady rise in undergraduate grades from 1973 to 1997. Subsequent reports and discussion from

17020-486: The lake's shore continues to serve as the headquarters for Princeton rowing. Princeton's grounds were designed by Beatrix Farrand between 1912 and 1943. Her contributions were most recently recognized with the naming of a courtyard for her. Subsequent changes to the landscape were introduced by Quennell Rothschild & Partners in 2000. In 2005, Michael Van Valkenburgh was hired as the new consulting landscape architect for Princeton's 2016 Campus Plan. Lynden B. Miller

17168-453: The land was converted to commercial and residential spaces. Robert Goheen would succeed Dodds by unanimous vote and serve as president until 1972. Goheen's presidency was characterized as being more liberal than previous presidents, and his presidency would see a rise in Black applicants, as well as the eventual coeducation of the university in 1969. During this period of rising diversity,

17316-490: The largest libraries in the colonies. In 1756, the college moved again to its present home in Princeton, New Jersey , because Newark was felt to be too close to New York. Princeton was chosen for its location in central New Jersey and by strong recommendation by Belcher. The college's home in Princeton was Nassau Hall , named for the royal William III of England , a member of the House of Orange-Nassau . The trustees of

17464-447: The library. In 1961, Princeton admitted its first female graduate student, Sabra Follett Meservey, who would go on to be the first woman to earn a master's degree at Princeton. Meservey was, at the time of her admission, already a member of the faculty at Douglass College within Princeton. The dean of the graduate school issued a statement clarifying that Meservey's admission was an exception, and that "Princeton may permit other women in

17612-438: The new academic year starting September 2024 with administrators facing calls for resignation from faculty. Princeton explicitly prohibited the admission of women from its founding in 1746 until 1969. Since it lacked an affiliated women's college, it was often referred to as a "monastery", both lovingly and derisively, by members of the Princeton community. For about a decade, from 1887 to 1897, nearby Evelyn College for Women

17760-449: The office of the university president and other administrative offices. To the south of Nassau Hall lies a courtyard that is known as Cannon Green. Buried in the ground at the center is the "Big Cannon", which was left in Princeton by British troops as they fled following the Battle of Princeton. It remained in Princeton until the War of 1812 , when it was taken to New Brunswick . In 1836,

17908-709: The other two give consistent but less physically interesting theories in low dimensions. Topological string theory is not found in this classification because for it the spin-statistics theorem does not hold in the conformal gauge which was required in the full argument. A string worldsheet is a two dimensional surface which can be parameterized by two coordinates ( σ 1 , σ 2 ) {\displaystyle (\sigma _{1},\sigma _{2})} where σ 2 {\displaystyle \sigma _{2}} describes Euclidean time while σ 1 {\displaystyle \sigma _{1}} parameterize

18056-496: The peace treaty between the colonies and the British. The college did suffer from the revolution, with a depreciated endowment and hefty repair bills for Nassau Hall. In 1795, President Samuel Stanhope Smith took office, the first alumnus to become president. Nassau Hall suffered a large fire that destroyed its interior in 1802, which Smith blamed on rebellious students. The college raised funds for reconstruction, as well as

18204-486: The permanent location of the Graduate School and the elimination of the eating clubs, which he proposed replacing with quadrangles, a precursor to the residential college system. Wilson also continued to keep Princeton closed off from accepting Black students. When an aspiring Black student wrote a letter to Wilson, he got his secretary to reply telling him to attend a university where he would be more welcome. John Grier Hibben became president in 1912, and would remain in

18352-427: The possible massless and tachyonic states of the RNS string. For the closed strings, the physical states are the various combinations of these four sectors as left and right-moving sectors. The resulting string has a mass-shell condition of where N {\displaystyle N} is the level, counting the creation operators used to create the state. The resulting states can again be classified according to

18500-512: The post for two decades. On October 2, 1913, the Princeton University Graduate College was dedicated. When the United States entered World War I in 1917, Hibben allocated all available University resources to the government. As a result, military training schools opened on campus and laboratories and other facilities were used for research and operational programs. Overall, more than 6,000 students served in

18648-463: The practice for the future. Wilson further reformed the educational system by introducing the preceptorial system in 1905, a then-unique concept in the United States that augmented the standard lecture method of teaching with a more personal form in which small groups of students, or precepts, could interact with a single instructor, or preceptor, in their field of interest. The changes brought about many new faculty and cemented Princeton's academics for

18796-634: The predecessor of the university, the idea has been rebuked by Princeton historians. The founding of the university itself originated from a split in the Presbyterian church following the Great Awakening . In 1741, New Light Presbyterians were expelled from the Synod of Philadelphia in defense of how the Log College ordained ministers. The four founders of the College of New Jersey, who were New Lights, were either expelled or withdrew from

18944-408: The presidency in 1888, and although his election was not met by unanimous enthusiasm, he was well received by undergraduates. Patton's administration was marked by great change, for Princeton's enrollment and faculty had doubled. At the same time, the college underwent large expansion and social life was changing in reflection of the rise in eating clubs and burgeoning interest in athletics. In 1893,

19092-564: The report culminated to when in 2004, Nancy Weiss Malkiel , the dean of the college, implemented a grade deflation policy to address the findings. Malkiel's reason for the policy was that an A was becoming devalued as a larger percentage of the student body received one. Following its introduction, the number of A's and average GPA on campus dropped, although A's and B's were still the most frequent grades awarded. The policy received mixed approval from both faculty and students when first instituted. Criticism for grade deflation continued through

19240-410: The school was open to those of any religious denomination, with many of the founders being of Presbyterian faith, the college became the educational and religious capital of Scotch-Irish Presbyterian America. In 1747, following the death of then President Jonathan Dickinson, the college moved from Elizabeth to Newark, New Jersey , as that was where presidential successor Aaron Burr Sr. 's parsonage

19388-468: The states. These states are classified by what spin representation of the SO ( 8 ) {\displaystyle {\text{SO}}(8)} group they belong to, which is the rotation subgroup of the ten dimensional Lorentz group SO ( 1 , 9 ) ⊃ SO ( 1 , 1 ) SO ( 8 ) {\displaystyle {\text{SO}}(1,9)\supset {\text{SO}}(1,1){\text{SO}}(8)} . In particular,

19536-712: The string at an instance in time. For closed strings σ 1 ∼ σ 1 + 2 π {\displaystyle \sigma _{1}\sim \sigma _{1}+2\pi } while for open strings σ 1 ∈ [ 0 , π ] {\displaystyle \sigma _{1}\in [0,\pi ]} . Two other coordinate systems are often employed, these being complex coordinates ( w , w ¯ ) {\displaystyle (w,{\bar {w}})} defined by w = σ 1 + i σ 2 {\displaystyle w=\sigma _{1}+i\sigma _{2}} or

19684-501: The tachyonic NS− is a singlet while the NS+ state is a vector denoted by 8 v {\displaystyle 8_{v}} . The R+ sector Majorana–Weyl spinors belong to the 8 {\displaystyle 8} representation while the R− belong to the 8 ′ {\displaystyle 8'} representation. For open strings, the NS+, NS−, R+, and R− form

19832-532: The trustees elected Jonathan Dickinson as president and opened in Elizabeth, New Jersey , where classes were held in Dickinson's parsonage . With its founding, it became the fourth-oldest institution of higher education in the United States, and one of nine colonial colleges chartered before the American Revolution . The founders aimed for the college to have an expansive curriculum to teach people of various professions, not solely ministerial work. Though

19980-483: The trustees of the college to become the eighth president. After the liberal tenure of Smith, Green represented the conservative "Old Side", in which he introduced rigorous disciplinary rules and heavily embraced religion. Even so, believing the college was not religious enough, he took a prominent role in establishing the Princeton Theological Seminary next door. While student riots were

20128-433: The two fermionic fields are ( 1 / 2 , 0 ) {\displaystyle (1/2,0)} and ( 0 , 1 / 2 ) {\displaystyle (0,1/2)} while that of the bosonic fields is ( 0 , 0 ) {\displaystyle (0,0)} . The holomorphic stress-energy tensor has weight ( 2 , 0 ) {\displaystyle (2,0)} and

20276-473: The university could become an "institution against expansion of the war." Princeton's protests would taper off later that year, with The Daily Princetonian saying that, "Princeton 1970–71 was an emotionally burned out university." In 1982, the residential college system was officially established under Goheen's successor William G. Bowen , who would serve until 1988. During his presidency, Princeton's endowment increased from $ 625 million to $ 2 billion, and

20424-712: The university through the American Civil War . When Nassau Hall burned down again in 1855, Maclean raised funds and used the money to rebuild Nassau Hall and run the university on an austerity budget during the war years. With a third of students from the college being from the South, enrollment fell. Once many of the Southerners left, the campus became a sharp proponent for the Union , even bestowing an honorary degree to President Lincoln . James McCosh became

20572-586: The university's supervising architect, Ralph Adams Cram , the Collegiate Gothic style remained the standard for all new building on the Princeton campus until 1960. A flurry of construction projects in the 1960s produced a number of new buildings on the south side of the main campus, many of which have been poorly received. Several prominent architects have contributed some more recent additions, including Frank Gehry (Lewis Library), I. M. Pei (Spelman Halls), Demetri Porphyrios ( Whitman College ,

20720-422: The university's supervising architect, designed the chapel, which he viewed as the crown jewel for the Collegiate Gothic motif he had championed for the campus. At the time of its construction, it was the second largest university chapel in the world, after King's College Chapel, Cambridge . It underwent a two-year, $ 10 million restoration campaign between 2000 and 2002. The Chapel seats around 2,000 and serves as

20868-488: The volume of the gauge group V G {\displaystyle V_{G}} . BRST quantization proceeds by gauge fixing the path integral via the Fadeev–Popov procedure , which gives rise to a ghost action in addition to the now gauge fixed action. The RNS model originates from using the ( 1 , 1 ) {\displaystyle (1,1)} supergravity action which upon gauge fixing gives

21016-584: The years after the war, with the construction of Firestone Library in 1948 and the establishment of the Forrestal Research Center in nearby Plainsboro Township in the 1950s. Government sponsored research increased sharply, particularly in the physics and engineering departments, with much of it occurring at the new Forrestal campus. Though, as the years progressed, scientific research at the Forrestal campus declined, and in 1973, some of

21164-430: Was Nassau Hall, completed in 1756, and situated on the northern edge of the campus facing Nassau Street. The campus expanded steadily around Nassau Hall during the early and middle 19th century. The McCosh presidency (1868–88) saw the construction of a number of buildings in the High Victorian Gothic and Romanesque Revival styles, although many of them are now gone, leaving the remaining few to appear out of place. At

21312-616: Was invited to work with him as Princeton's consulting gardening architect, focusing on the 17 gardens that are distributed throughout the campus. Nassau Hall is the oldest building on campus. Begun in 1754 and completed in 1756, it was the first seat of the New Jersey Legislature in 1776, was involved in the Battle of Princeton in 1777, and was the seat of the Congress of the Confederation (and thus capitol of

21460-526: Was largely composed of daughters of professors and sisters of Princeton undergraduates. While no legal connection existed, many Princeton professors taught there and several Princeton administrators, such as Francis Patton, were on its board of trustees. It closed in 1897 following the death of its founder, Joshua McIlvaine . In 1947, three female members of the library staff enrolled in beginning Russian courses to deal with an increase in Russian literature in

21608-427: Was located. That same year, Princeton's first charter came under dispute by Anglicans, but on September 14, 1748, the recently appointed governor Jonathan Belcher granted a second charter. Belcher, a Congregationalist , had become alienated from his alma mater , Harvard, and decided to "adopt" the infant college. Belcher would go on to raise funds for the college and donate his 474-volume library, making it one of

21756-406: Was only a professor at the time, recommended saving the university with the help of alumni; as a result, Princeton's alumni association, led by James Madison , was created and began raising funds. With Carnahan and Maclean, now vice-president, working as partners, enrollment and faculty increased, tensions decreased, and the college campus expanded. Maclean took over the presidency in 1854, and led

21904-478: Was shaped much in its formative years by the " Log College ", a seminary founded by the Reverend William Tennent at Neshaminy, Pennsylvania , in about 1726. While no legal connection ever existed, many of the pupils and adherents from the Log College would go on to financially support and become substantially involved in the early years of the university. While early writers considered it as

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