
Spontaneous symmetry breaking is a mode of realization of symmetry breaking in a physical system, where the underlying laws are invariant under a symmetry transformation, but the system as a whole changes under such transformations, in contrast to explicit symmetry breaking. It is a spontaneous process by which a system in a symmetrical state ends up in an asymmetrical state. It thus describes systems where the equations of motion or the Lagrangian obey certain symmetries, but the lowest energy solutions do not exhibit that symmetry.
Consider the bottom of an empty wine bottle, a symmetrical upward dome with a gutter for sediment. If a ball is placed at the peak of the dome, the situation is symmetrical with respect to rotating the wine bottle. But the ball may spontaneously break this symmetry and roll into the gutter, a point of lowest energy. The bottle and the ball retain their symmetry, but the system does not.[1]
Most simple phases of matter and phasetransitions, like crystals, magnets, and conventional superconductors can be simply understood from the viewpoint of spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the fractional quantum Hall effect.
Spontaneous symmetry breaking in physics
[edit]Particle physics
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 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 the symmetry of the underlying theory. "Hidden" is perhaps a better term than "broken" because the symmetry is always there in these equations. This phenomenon is called spontaneous symmetry breaking because nothing (that we know) breaks the symmetry in the equations.[2]
[edit]Chiral symmetry
Chiral symmetry breaking 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
ambu–Goldstone bosons in this spontaneous symmetry breaking process are 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.
[edit]Higgs mechanism
The strong, weak, and electromagnetic forces can all be understood as arising from gauge symmetries. The Higgs mechanism, the spontaneoussymmetry breaking of gauge symmetries, is important component in understanding the superconductivity of metals and the origin of particle masses in the standard model of particlephysics. One important consequence of the distinction between true symmetries and gauge symmetries, is that the spontaneous breaking of a gauge symmetry does not gives rise to characteristic massless NambuGoldstone modes, but only massive modes, like the plasmamode in a superconductor, or the Higgs mode observed in particle physics.
In the standard model of particle physics, spontaneous symmetry breaking of the SU(2)xU(1) gaugesymmetry associated with the electroweak force generates masses for several particles, and separates the electromagnetic and weak forces. The W and Z bosons are the elementary particles which 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 is broken so that the photon and the massive W and Z bosons emerge.[3] 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 is augmented by the Higgs mechanism to give these particles mass. It also suggests the presence of a new particle, the Higgs boson, reported as possibly identifiable with a boson detected in 2012. (If the Higgs boson were not confirmed to have been found, it would mean that the simplest implementation of the Higgs mechanism and spontaneous symmetry breaking as they are currently formulated require modification.)
A detailed presentation of the Higgs mechanism is given in the article on the Yukawa interaction, illustrating how it further gives mass to fermions.
Superconductivity of metals is a condensedmatter 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.

