# Spontaneous symmetry breaking

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetrical state ends up in an asymmetrical state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry.

## Quotes

* 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 scalar mesons. 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.
** Sidney Coleman and Erick Weinberg: (1973). "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking". Physical Review D 7 (6): 1888–1910. DOI:10.1103/PhysRevD.7.1888.
* The observed CP violation 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.
** T. D. Lee: (1974). "CP nonconservation and spontaneous symmetry breaking". Physics Reports 9 (2): 143–177. ISSN 03701573. DOI:10.1016/0370-1573(74)90020-9.
* 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.
** C. N. Leung, S. T. Love, and William A. Bardeen: (1986). "Spontaneous symmetry breaking in scale invariant quantum electrodynamics". Nuclear Physics B 273 (3–4): 649–662. DOI:10.1016/0550-3213(86)90382-2.
* The Ward-Takahashi identities 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 S-matrix 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.
** N. K. Nielsen: (1975). "On the gauge dependence of spontaneous symmetry breaking in gauge theories". Nuclear Physics B 101 (1): 173–188. DOI:10.1016/0550-3213(75)90301-6.
* 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.
** Stephen Webb (25 May 2004). Out of this World: Colliding Universes, Branes, Strings, and Other Wild Ideas of Modern Physics. Springer Science & Business Media. p. 101. ISBN 978-0-387-02930-6.