An Axiomatic Approach to Semiclassical Perturbative Gauge Field Theories

TL;DR

This paper develops an axiomatic framework for semiclassical perturbative gauge field theories, exploring states, transformations, and actions, and applying the theory to electrodynamics and non-Abelian gauge theories.

Contribution

It introduces a comprehensive axiomatic approach to semiclassical gauge theories, linking various formalisms and extending perturbation theory within this framework.

Findings

Constructed semiclassical perturbation theory.

Analyzed relation with S-matrix theory.

Studied semiclassical electrodynamics and non-Abelian gauge theories.

Abstract

Different approaches to axionatic field theory are investigated. The main notions of semiclassical theory are the following: semiclassical states, Poincare transformations, semiclassical action form, semiclassical gauge equivalence and semiclassical field. If the manifestly covariant approach is used, the notion of semiclassical state is related to Schwinger sourse, while the semicalssical action is presented via the R-function of Lehmann, Symanzik and Zimmermann. Semiclassical perturbation theory is constructed. Its relation with the S-matrix theory is investigated. Semiclassical electrodynamics and non-Abelian gauge theories are studied, making us of the Gupta-Bleuler and BRST approaches.