Symmetries III: Global symmetries in field theory

Abstract

This chapter examines the role of global symmetries in local quantum field theories. It shows that exact global symmetries are rare — indeed, if we take gravitational effects into account, probably non-existent. Nevertheless, approximate global symmetries play an enormously important role in modern field theory. The appearance of massless Goldstone particles once an exact global symmetry is spontaneously broken is of enormous importance in modern field theory, and proof of the Goldstone theorem embodying this phenomenon is given. Dynamical aspects of spontaneous symmetry-breaking (SSB) are examined, and it is shown that the essence of SSB resides in the energetics of the theory in the infrared (i.e., at long distances).