Divergence identity and the dynamical rearrangement of symmetry in the conventional field theory

Abstract

The canonical equation of motion is rewritten in an alternative form, and a divergence identity is derived. It is shown that the generalized Ward identity is a special case of the general divergence identity. The use of the divergence identity together with the Haag-Nishijima-Zimmermann construction theorem is illustrated with the Nambu-Jona-Lasinio model. It is proved without any approximation, within the framework of the conventional field theory, that the Goldstone boson carries the chiral gauge transformation.