Spontaneous symmetry breaking
physical phenomenon in which the vacuum expectation value of a field is not invariant under a symmetry of the action, so that a symmetry present at high temperatures is broken at low temperatures
Spontaneous symmetry breaking (SSB) 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 the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions or ground states 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.
Overview
The spontaneous symmetry breaking cannot happen in quantum mechanics that describes finite dimensional systems, due to Stone-von Neumann theorem (that states the uniqueness of Heisenberg commutation relations in finite dimensions). So spontaneous symmetry breaking can be observed only 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 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 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.
This brief starts where responsible research should: with the source description of “Spontaneous symmetry breaking” as physical phenomenon in which the vacuum expectation value of a field is not invariant under a symmetry of the action, so that a symmetry present at high temperatures is broken at low temperatures. Everything that follows is an evidence route, not borrowed authority.
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The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Aug 19, 2026. The linked authority identifier is Q736716. None of the 0 selected statements returned an explicit reference.
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This entry incorporates text from “Spontaneous symmetry breaking” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.