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69-599: During the quark epoch (shortly after the Big Bang ), the electroweak force split into the electromagnetic and weak force . It is thought that the required temperature of 10 K has not been seen widely throughout the universe since before the quark epoch, and currently the highest human-made temperature in thermal equilibrium is around 5.5 × 10 K (from the Large Hadron Collider ). Sheldon Glashow , Abdus Salam , and Steven Weinberg were awarded

138-614: A vacuum state of the full quantum theory , although a classical solution may break a continuous symmetry. On October 7, 2008, the Royal Swedish Academy of Sciences awarded the 2008 Nobel Prize in Physics to three scientists for their work in subatomic physics symmetry breaking. Yoichiro Nambu , of the University of Chicago , won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in

207-493: A continuous symmetry is inevitably accompanied by gapless (meaning that these modes do not cost any energy to excite) Nambu–Goldstone modes associated with slow, long-wavelength fluctuations of the order parameter. For example, vibrational modes in a crystal, known as phonons, are associated with slow density fluctuations of the crystal's atoms. The associated Goldstone mode for magnets are oscillating waves of spin known as spin-waves. For symmetry-breaking states, whose order parameter

276-441: A massless, neutral gauge boson . Initially rejecting such a particle as useless, he later realized his symmetries produced the electroweak force, and he proceeded to predict rough masses for the W and Z bosons . Significantly, he suggested this new theory was renormalizable. In 1971, Gerard 't Hooft proved that spontaneously broken gauge symmetries are renormalizable even with massive gauge bosons. Mathematically, electromagnetism

345-478: A pair of outcomes can be different. For example in an electric field, the forces on a charged particle are different in different directions, so the rotational symmetry is explicitly broken by the electric field which does not have this symmetry. Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like

414-525: A singlet), and, instead changes under the (hidden) symmetry, now implemented in the (nonlinear) Nambu–Goldstone mode . Normally, in the absence of the Higgs mechanism, massless Goldstone bosons arise. The symmetry group can be discrete, such as the space group of a crystal, or continuous (e.g., a Lie group ), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in

483-411: A specific stable vacuum state (amounting to a choice of θ ), this symmetry will appear to be lost, or "spontaneously broken". In fact, any other choice of θ would have exactly the same energy, and the defining equations respect the symmetry but the ground state (vacuum) of the theory breaks the symmetry, implying the existence of a massless Nambu–Goldstone boson , the mode running around the circle at

552-417: Is where   q f   {\displaystyle \ q_{f}\ } is the fermions' electric charges. The neutral weak current   J μ 3   {\displaystyle \ J_{\mu }^{3}\ } is where T f 3 {\displaystyle T_{f}^{3}} is the fermions' weak isospin. The charged current part of

621-405: Is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., Lagrangian ). Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of

690-519: Is an example of spontaneous symmetry breaking affecting the chiral symmetry of the strong interactions in particle physics. It is a property of quantum chromodynamics , the quantum field theory describing these interactions, and is responsible for the bulk of the mass (over 99%) of the nucleons , and thus of all common matter, as it converts very light bound quarks into 100 times heavier constituents of baryons . The approximate Nambu–Goldstone bosons in this spontaneous symmetry breaking process are

759-478: Is an important component in understanding the superconductivity of metals and the origin of particle masses in the standard model of particle physics. The term "spontaneous symmetry breaking" is a misnomer here as Elitzur's theorem states that local gauge symmetries can never be spontaneously broken. Rather, after gauge fixing, the global symmetry (or redundancy) can be broken in a manner formally resembling spontaneous symmetry breaking. One important consequence of

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828-514: Is augmented by the Higgs mechanism to give these particles mass. It also suggests the presence of a new particle, the Higgs boson , detected in 2012. Superconductivity of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism. Dynamical symmetry breaking (DSB)

897-471: Is best described by breaking it up into several parts as follows. The kinetic term L K {\displaystyle {\mathcal {L}}_{K}} contains all the quadratic terms of the Lagrangian, which include the dynamic terms (the partial derivatives) and the mass terms (conspicuously absent from the Lagrangian before symmetry breaking) where the sum runs over all the fermions of

966-512: Is broken so that the photon and the massive W and Z bosons emerge. In addition, fermions develop mass consistently. Without spontaneous symmetry breaking, the Standard Model of elementary particle interactions requires the existence of a number of particles. However, some particles (the W and Z bosons ) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking

1035-409: Is known as the hadron epoch . This physical cosmology -related article is a stub . You can help Misplaced Pages by expanding it . Spontaneous symmetry breaking Spontaneous symmetry breaking is a spontaneous process of symmetry breaking , by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where

1104-399: Is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity. An important theorem, due to Mermin and Wagner, states that, at finite temperature, thermally activated fluctuations of Nambu–Goldstone modes destroy the long-range order, and prevent spontaneous symmetry breaking in one- and two-dimensional systems. Similarly, quantum fluctuations of

1173-432: Is not invariant under the symmetry in question, we say that the system is in the ordered phase , and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter, which specifies a "frame of reference" to be measured against. In that case, the vacuum state does not obey the initial symmetry (which would keep it invariant, in the linearly realized Wigner mode in which it would be

1242-468: Is often due to creation of a fermionic condensate — e.g., the quark condensate , which is connected to the dynamical breaking of chiral symmetry in quantum chromodynamics . Conventional superconductivity is the paradigmatic example from the condensed matter side, where phonon-mediated attractions lead electrons to become bound in pairs and then condense, thereby breaking the electromagnetic gauge symmetry. Most phases of matter can be understood through

1311-479: Is spontaneously broken as h → 0 when the Hamiltonian becomes invariant under the inversion transformation, but the expectation value is not invariant. Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization. Spontaneous breaking of

1380-725: Is the vacuum expectation value. The   L y   {\displaystyle \ {\mathcal {L}}_{y}\ } term describes the Yukawa interaction with the fermions, and generates their masses, manifest when the Higgs field acquires a nonzero vacuum expectation value, discussed next. The   y k i j   , {\displaystyle \ y_{k}^{ij}\ ,} for   k ∈ { u , d , e }   , {\displaystyle \ k\in \{\mathrm {u,d,e} \}\ ,} are matrices of Yukawa couplings. The Lagrangian reorganizes itself as

1449-428: Is the weak hypercharge and the   T j   {\displaystyle \ T_{j}\ } are the components of the weak isospin. The L h {\displaystyle {\mathcal {L}}_{h}} term describes the Higgs field h {\displaystyle h} and its interactions with itself and the gauge bosons, where v {\displaystyle v}

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1518-452: Is unified with the weak interactions as a Yang–Mills field with an SU(2) × U(1) gauge group , which describes the formal operations that can be applied to the electroweak gauge fields without changing the dynamics of the system. These fields are the weak isospin fields W 1 , W 2 , and W 3 , and the weak hypercharge field B . This invariance is known as electroweak symmetry . The generators of SU(2) and U(1) are given

1587-404: The Higgs boson . That is to say: the Higgs and the electromagnetic field have no effect on each other, at the level of the fundamental forces ("tree level"), while any other combination of the hypercharge and the weak isospin must interact with the Higgs. This causes an apparent separation between the weak force, which interacts with the Higgs, and electromagnetism, which does not. Mathematically,

1656-526: The SU(2) × U(1) gauge symmetry associated with the electro-weak force generates masses for several particles, and separates the electromagnetic and weak forces. The W and Z bosons are the elementary particles that mediate the weak interaction , while the photon mediates the electromagnetic interaction . At energies much greater than 100 GeV, all these particles behave in a similar manner. The Weinberg–Salam theory predicts that, at lower energies, this symmetry

1725-423: The W 3 and B bosons coalesce into two different physical bosons with different masses – the Z boson, and the photon ( γ ), where θ W is the weak mixing angle . The axes representing the particles have essentially just been rotated, in the ( W 3 , B ) plane, by the angle θ W . This also introduces a mismatch between the mass of the Z and

1794-421: The effective action ). Dynamical breaking of a gauge symmetry is subtler. In conventional spontaneous gauge symmetry breaking, there exists an unstable Higgs particle in the theory, which drives the vacuum to a symmetry-broken phase (i.e, electroweak interactions .) In dynamical gauge symmetry breaking, however, no unstable Higgs particle operates in the theory, but the bound states of the system itself provide

1863-534: The equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry . When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry. The spontaneous symmetry breaking cannot happen in quantum mechanics that describes finite dimensional systems, due to Stone-von Neumann theorem (that states

1932-400: The fractional quantum Hall effect . Typically, when spontaneous symmetry breaking occurs, the observable properties of the system change in multiple ways. For example the density, compressibility, coefficient of thermal expansion, and specific heat will be expected to change when a liquid becomes a solid. Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at

2001-451: The pions , whose mass is an order of magnitude lighter than the mass of the nucleons. It served as the prototype and significant ingredient of the Higgs mechanism underlying the electroweak symmetry breaking. The strong, weak, and electromagnetic forces can all be understood as arising from gauge symmetries , which is a redundancy in the description of the symmetry. The Higgs mechanism , the spontaneous symmetry breaking of gauge symmetries,

2070-407: The strong interaction and the weak interaction had taken their present forms, but the temperature of the universe was still too high to allow quarks to bind together to form hadrons . The quark epoch began approximately 10 seconds after the Big Bang , when the preceding electroweak epoch ended as the electroweak interaction separated into the weak interaction and electromagnetism. During

2139-465: The weak interaction , a search began for a way to relate the weak and electromagnetic interactions . Extending his doctoral advisor Julian Schwinger 's work, Sheldon Glashow first experimented with introducing two different symmetries, one chiral and one achiral, and combined them such that their overall symmetry was unbroken. This did not yield a renormalizable theory , and its gauge symmetry had to be broken by hand as no spontaneous mechanism

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2208-518: The 1979 Nobel Prize in Physics for their contributions to the unification of the weak and electromagnetic interaction between elementary particles , known as the Weinberg–Salam theory . The existence of the electroweak interactions was experimentally established in two stages, the first being the discovery of neutral currents in neutrino scattering by the Gargamelle collaboration in 1973, and

2277-505: The Higgs field acquires a non-vanishing vacuum expectation value dictated by the potential of the previous section. As a result of this rewriting, the symmetry breaking becomes manifest. In the history of the universe, this is believed to have happened shortly after the hot big bang, when the universe was at a temperature 159.5 ± 1.5  GeV (assuming the Standard Model of particle physics). Due to its complexity, this Lagrangian

2346-516: The Higgs three-point and four-point self interaction terms, L H V {\displaystyle {\mathcal {L}}_{\mathrm {HV} }} contains the Higgs interactions with gauge vector bosons, L W W V {\displaystyle {\mathcal {L}}_{\mathrm {WWV} }} contains the gauge three-point self interactions, L W W V V {\displaystyle {\mathcal {L}}_{\mathrm {WWVV} }} contains

2415-515: The Lagrangian contain the interactions between the fermions and gauge bosons, where   e = g   sin ⁡ θ W = g ′   cos ⁡ θ W   . {\displaystyle ~e=g\ \sin \theta _{\mathrm {W} }=g'\ \cos \theta _{\mathrm {W} }~.} The electromagnetic current J μ e m {\displaystyle \;J_{\mu }^{\mathrm {em} }\;}

2484-518: The Lagrangian is given by where   ν   {\displaystyle \ \nu \ } is the right-handed singlet neutrino field, and the CKM matrix M i j C K M {\displaystyle M_{ij}^{\mathrm {CKM} }} determines the mixing between mass and weak eigenstates of the quarks. L H {\displaystyle {\mathcal {L}}_{\mathrm {H} }} contains

2553-423: The associated Higgs mechanism . In the Standard Model , the observed physical particles, the W and Z bosons , and the photon , are produced through the spontaneous symmetry breaking of the electroweak symmetry SU(2) × U(1) Y to U(1) em , effected by the Higgs mechanism (see also Higgs boson ), an elaborate quantum-field-theoretic phenomenon that "spontaneously" alters

2622-513: The case of spontaneous symmetry breaking, there is not a general framework for describing such states. The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins below the Curie temperature and at h = 0 , where h is the external magnetic field. Below the Curie temperature , the energy of the system is invariant under inversion of the magnetization m ( x ) such that m ( x ) = − m (− x ) . The symmetry

2691-417: The context of the strong interactions, specifically chiral symmetry breaking . Physicists Makoto Kobayashi and Toshihide Maskawa , of Kyoto University , shared the other half of the prize for discovering the origin of the explicit breaking of CP symmetry in the weak interactions. This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not

2760-421: The distinction between true symmetries and gauge symmetries , is that the massless Nambu–Goldstone resulting from spontaneous breaking of a gauge symmetry are absorbed in the description of the gauge vector field, providing massive vector field modes, like the plasma mode in a superconductor, or the Higgs mode observed in particle physics. In the standard model of particle physics, spontaneous symmetry breaking of

2829-451: The electric charge is a specific combination of the hypercharge and T 3 outlined in the figure. U(1) em (the symmetry group of electromagnetism only) is defined to be the group generated by this special linear combination, and the symmetry described by the U(1) em group is unbroken, since it does not directly interact with the Higgs. The above spontaneous symmetry breaking makes

Electroweak interaction - Misplaced Pages Continue

2898-401: The equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A by the same amount . The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions. An actual measurement reflects only one solution, representing a breakdown in

2967-489: The gauge four-point self interactions,   L Y   {\displaystyle \ {\mathcal {L}}_{\mathrm {Y} }\ } contains the Yukawa interactions between the fermions and the Higgs field, Quark epoch In physical cosmology , the quark epoch was the period in the evolution of the early universe when the fundamental interactions of gravitation , electromagnetism ,

3036-407: The interaction between the three W vector bosons and the B vector boson, where W a μ ν {\displaystyle W_{a}^{\mu \nu }} ( a = 1 , 2 , 3 {\displaystyle a=1,2,3} ) and B μ ν {\displaystyle B^{\mu \nu }} are the field strength tensors for

3105-463: The left-handed doublet and right-handed singlet electron fields. The Feynman slash D / {\displaystyle D\!\!\!\!/} means the contraction of the 4-gradient with the Dirac matrices , defined as and the covariant derivative (excluding the gluon gauge field for the strong interaction ) is defined as Here   Y   {\displaystyle \ Y\ }

3174-823: The lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific direction, breaking rotational symmetry . In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals , charge- and spin-density waves, superfluids, and many others. There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as fractional quantum Hall liquids , and spin-liquids . These states do not break any symmetry, but are distinct phases of matter. Unlike

3243-450: The mass of the W particles (denoted as m Z and m W , respectively), The W 1 and W 2 bosons, in turn, combine to produce the charged massive bosons W : The Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking becomes manifest, The L g {\displaystyle {\mathcal {L}}_{g}} term describes

3312-419: The minimum of this potential, and indicating there is some memory of the original symmetry in the Lagrangian. In particle physics , the force carrier particles are normally specified by field equations with gauge symmetry ; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving

3381-424: The name weak isospin (labeled T ) and weak hypercharge (labeled Y ) respectively. These then give rise to the gauge bosons that mediate the electroweak interactions – the three W bosons of weak isospin ( W 1 , W 2 , and W 3 ), and the B boson of weak hypercharge, respectively, all of which are "initially" massless. These are not physical fields yet, before spontaneous symmetry breaking and

3450-543: The order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero temperature. (An important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantity and does not have any quantum fluctuations.) Other long-range interacting systems, such as cylindrical curved surfaces interacting via the Coulomb potential or Yukawa potential , have been shown to break translational and rotational symmetries. It

3519-471: The quark epoch, the universe was filled with a dense, hot quark–gluon plasma , containing quarks, leptons and their antiparticles . Collisions between particles were too energetic to allow quarks to combine into mesons or baryons . The quark epoch ended when the universe was about 10 seconds old, when the average energy of particle interactions had fallen below the binding energy of hadrons. The following period, when quarks became confined within hadrons,

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3588-409: The realization of the symmetry and rearranges degrees of freedom. The electric charge arises as the particular linear combination (nontrivial) of Y W (weak hypercharge) and the T 3 component of weak isospin ( Q = T 3 + 1 2 Y W {\displaystyle Q=T_{3}+{\tfrac {1}{2}}\,Y_{\mathrm {W} }} ) that does not couple to

3657-407: The relevant homotopy group and the dynamics of the theory. For example, Higgs symmetry breaking may have created primordial cosmic strings as a byproduct. Hypothetical GUT symmetry-breaking generically produces monopoles , creating difficulties for GUT unless monopoles (along with any GUT domain walls) are expelled from our observable Universe through cosmic inflation . Chiral symmetry breaking

3726-576: The relevant field ( A , {\displaystyle A,} Z , {\displaystyle Z,} W ± {\displaystyle W^{\pm }} ) and f  by the structure constants of the appropriate gauge group. The neutral current   L N   {\displaystyle \ {\mathcal {L}}_{\mathrm {N} }\ } and charged current   L C   {\displaystyle \ {\mathcal {L}}_{\mathrm {C} }\ } components of

3795-431: The same probability distribution. For example if measurements of an observable at any two different positions have the same probability distribution, the observable has translational symmetry. Spontaneous symmetry breaking occurs when this relation breaks down, while the underlying physical laws remain symmetrical. Conversely, in explicit symmetry breaking , if two outcomes are considered, the probability distributions of

3864-603: The second in 1983 by the UA1 and the UA2 collaborations that involved the discovery of the W and Z gauge bosons in proton–antiproton collisions at the converted Super Proton Synchrotron . In 1999, Gerardus 't Hooft and Martinus Veltman were awarded the Nobel prize for showing that the electroweak theory is renormalizable . After the Wu experiment in 1956 discovered parity violation in

3933-408: The spontaneously broken symmetry is summarized through an illustrative scalar field theory . The relevant Lagrangian of a scalar field ϕ {\displaystyle \phi } , which essentially dictates how a system behaves, can be split up into kinetic and potential terms, It is in this potential term V ( ϕ ) {\displaystyle V(\phi )} that

4002-399: The symmetry breaking is triggered. An example of a potential, due to Jeffrey Goldstone is illustrated in the graph at the left. This potential has an infinite number of possible minima (vacuum states) given by for any real θ between 0 and 2 π . The system also has an unstable vacuum state corresponding to Φ = 0 . This state has a U(1) symmetry. However, once the system falls into

4071-583: The symmetry of the underlying theory. "Hidden" is a better term than "broken", because the symmetry is always there in these equations. This phenomenon is called spontaneous symmetry breaking (SSB) because nothing (that we know of) breaks the symmetry in the equations. By the nature of spontaneous symmetry breaking, different portions of the early Universe would break symmetry in different directions, leading to topological defects , such as two-dimensional domain walls , one-dimensional cosmic strings , zero-dimensional monopoles , and/or textures , depending on

4140-400: The system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of

4209-783: The theory (quarks and leptons), and the fields   A μ ν   , {\displaystyle \ A_{\mu \nu }\ ,}   Z μ ν   , {\displaystyle \ Z_{\mu \nu }\ ,}   W μ ν −   , {\displaystyle \ W_{\mu \nu }^{-}\ ,} and   W μ ν + ≡ ( W μ ν − ) †   {\displaystyle \ W_{\mu \nu }^{+}\equiv (W_{\mu \nu }^{-})^{\dagger }\ } are given as with X {\displaystyle X} to be replaced by

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4278-430: The theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one. The crucial concept in physics theories is the order parameter . If there is a field (often a background field) which acquires an expectation value (not necessarily a vacuum expectation value ) which

4347-473: The underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the Goldstone boson .) When a theory is symmetric with respect to a symmetry group , but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate which member is distinct, only that one is . From this point on,

4416-442: The uniqueness of Heisenberg commutation relations in finite dimensions). So spontaneous symmetry breaking can just be observed in infinite dimensional theories, as quantum field theories . By definition, spontaneous symmetry breaking requires the existence of physical laws which are invariant under a symmetry transformation (such as translation or rotation), so that any pair of outcomes differing only by that transformation have

4485-430: The unstable fields that render the phase transition. For example, Bardeen, Hill, and Lindner published a paper that attempts to replace the conventional Higgs mechanism in the standard model by a DSB that is driven by a bound state of top-antitop quarks. (Such models, in which a composite particle plays the role of the Higgs boson, are often referred to as "Composite Higgs models".) Dynamical breaking of gauge symmetries

4554-431: The very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may spontaneously break this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not. In the simplest idealized relativistic model,

4623-496: The weak isospin and weak hypercharge gauge fields. L f {\displaystyle {\mathcal {L}}_{f}} is the kinetic term for the Standard Model fermions. The interaction of the gauge bosons and the fermions are through the gauge covariant derivative , where the subscript j sums over the three generations of fermions; Q , u , and d are the left-handed doublet, right-handed singlet up, and right handed singlet down quark fields; and L and e are

4692-404: Was known, but it predicted a new particle, the Z boson . This received little notice, as it matched no experimental finding. In 1964, Salam and John Clive Ward had the same idea, but predicted a massless photon and three massive gauge bosons with a manually broken symmetry. Later around 1967, while investigating spontaneous symmetry breaking , Weinberg found a set of symmetries predicting

4761-400: Was shown, in the presence of a symmetric Hamiltonian, and in the limit of infinite volume, the system spontaneously adopts a chiral configuration — i.e., breaks mirror plane symmetry . For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore symmetric with respect to these outcomes. However, if

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