Spontaneous symmetry breaking

"Symmetry is one of the great unifying themes in physics. From cosmology to and from to , symmetries determine which shapes, interactions, and evolutions occur in nature. Perhaps the most important aspect of symmetry in theories of physics, is the idea that the states of a system do not need to have the same symmetries as the theory that describes them. Such spontaneous breakdown of symmetries governs the dynamics of , the emergence of new particles and s, the rigidity of collective states of matter, and is one of the main ways emerges in a quantum world. The basic idea of spontaneous symmetry breaking is well known, and repeated in different ways throughout all fields of physics."

"We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless s. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson."

"The secret of nature is symmetry, but much of the texture of the world is due to mechanisms of symmetry breaking. The are a variety of mechanisms wherein the symmetry of nature can be hidden or broken. The first is explicit symmetry breaking where the is only approximately symmetric, but the magnitude of the symmetry breaking forces is small, so that one can treat the symmetry violation as a small correction. Such approximate symmetries lead to approximate conservation laws. Many of the symmetries observed in nature are of this sort, not really symmetries of the laws of physics at all, but—for what appears sometimes to be accidental reasons—approximate symmetries for a certain class of phenomena. The isotopic symmetry of the is an example of an approximate symmetry; good due to the small values of the and masses and the weakness of the electromagnetic force. A more profound way of hiding symmetry is the phenomenon of spontaneous symmetry breaking. Here the laws of physics are symmetric but the state of the system is not. This situation is common in . The is an example of a solution of Newton’s equations that is not rotationally invariant, although the equations are. Consequently, for an observer of the solar system, the rotational invariance of the law of gravitation is not manifest."

"The observed is assumed to be due to the spontaneous symmetry-breaking mechanism; the Lagrangian is CP invariant but its particular solution is not. The general classification of such theories when coupled with different unified gauge models of the weak and electromagnetic interactions is given. All such theories lead naturally to a basically milliweak CP noninvariant solution. The possibility that for most weak transitions the result may resemble a superweak theory is analysed, and possible experiments to distinguish these two different types of theories are discussed. Detailed calculations for various CP violating amplitudes are carried out for a generalized Georgi-Glashow model."

"Quantum electrodynamics is studied analytically in a quenched, planar approximation in four dimensions. At sufficiently strong coupling, chiral symmetry is broken spontaneously and the corresponding pseudoscalar Goldstone boson is observed. This phase of the theory is governed by a novel ultraviolet fixed point which requires the mixing of four-fermion interactions with the electrodynamic interactions."

"The for scalar electrodynamics in Fermi gauges are shown to imply a homogeneous first-order partial differential equation for the effective potential involving only the gauge parameter and the external scalar field. Spontaneous symmetry breaking is consequently a gauge-invariant phenomenon. Also observable quantities, including masses, physical coupling constants, and elements, of a theory with spontaneous symmetry breaking are found to be invariant, if a change in the gauge parameter is accompanied by a suitable change in the ground-state expectation value of the scalar field. The generalization to a non-Abelian gauge theory is briefly indicated."

"There is nothing mysterious about spontaneous symmetry breaking. There are many examples in physics. Hold a drinking straw between the palms of your hands and you have a physical system that can be described by equations possessing rotational symmetry. Press your palms together and the straw bends. The symmetry is broken. You cannot necessarily predict how the straw will bend; it could bend "up," "down," "sideways," or in any other direction. This unsymmetrical situation, however, is the stable solution of perfectly symmetrical equations."