Dynamical consequences of spontaneous breakdown of symmetries

The spontaneous breakdown of a continuous symmetry group generated by conserved currents is considered. In the framework of general quantum field theory the possible dynamical consequences of spontaneous breakdown are analysed: a general relation is derived between n− and (n+1) — point functions involving Goldstone bosons in the limit of zero momentum. The technique is illustrated by a few examples for the SU(2) × SU(2) chiral group and the results generalized relations known from the perturbative treatment of the σ-model.