The Goldstone Theorem

Abstract

The mechanism of SSB does not only provide a general strategy for unifying the description of apparently different systems, but it also provides information on the energy spectrum of an infinite dimensional system, by means of the so-called Goldstone theorem,⁴⁰ according to which to each broken generator T of a continuous symmetry there corresponds a massless mode, i.e. a free wave. The quantum version of such a statement has been turned into a theorem,⁴¹ whereas, as far as we know, no analogous theorem has been proved for classical (infinite dimensional) systems and the standard accounts seem to rely on heuristic arguments.