Conserved Currents, Their Commutators, and the Symmetry Structure of Renormalizable Theories of Electromagnetic, Weak, and Strong Interactions

This paper discusses the role played by conserved currents in fixing the structure of currently popular renormalizable theories of strong, electromagnetic, and weak interactions. The major objective of this work is to show that these theories correspond to another kind of symmetry-which we call a Higgs-type symmetry-and to clarify the relation of this scheme to the already familiar normal and Goldstone symmetries. In order to do this, we introduce a language which makes no reference to any specific Lagrangian formalism and so avoids questions of whether or not hadrons are composite and whether or not the Goldstone bosons (massless particles of these theories) necessarily have massive partners. For pedagogical reasons, we discuss the original Weinberg model of leptons and a model coupling leptons and hadrons from the current-algebra point of view.