Approximate Symmetry and Spontaneous Symmetry Breaking
In this short chapter we briefly discuss the formalism of approximate symmetry, based on the concept of a metric for a statejspace of a system. We present the concepts of approximate symmetry transformation, approximate symmetry group, goodness of approximation, exact symmetry limit, broken symmetry, and symmetry-breaking factor. We then more substantially discuss spontaneous symmetry breaking, situations where the symmetry principle—that the effect is at least as symmetric as the cause—seems to be invalid. The essence of the matter is the stability of the effect under perturbations of the symmetry of the cause.
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