= Spontaneous symmetry breaking
{title2=SSB}
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<Spontaneous symmetry breaking> occurs when the <action> and equations have a <symmetry> but a chosen <ground state> is invariant only under a proper <subgroup>. Acting with the broken <symmetry> generates a degenerate <vacuum manifold>. An <order parameter> distinguishes the selected states: the equations do not prefer its direction, yet a particular state does. This lets one use the <symmetry> of the laws to predict excitations around a state that has less <symmetry>, notably the <Goldstone bosons> of a broken <continuous symmetry>.
A finite system with <symmetry>-preserving <boundary conditions> can have a symmetric <ground state>; a symmetric statistical mixture of broken states also has vanishing mean <order parameter>. A nonzero mean therefore requires a stated selection procedure. The <symmetry-breaking order of limits> takes the <thermodynamic limit> in a small applied source before removing that source. The <finite-volume angular source selection> example makes the distinction explicit for a <continuous symmetry>.
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