Current Algebras, Sum Rules, and Canonical Field Theories

Abstract

A very large class of c-number Lagrangian field theories, called canonical field theories—being all theories whose field equations have sufficiently many solutions—satisfy a number of important completeness relations. These relations ensure the existence of Gell-Mann current algebras and Fubini sum rules, and guarantee that canonical field quantization is possible. We have studied finite-component, first- and second-order Largrangians in general, and a class of fourth-order Lagrangians. The work is preliminary to an investigation of infinite-component field theories.