Nonabelian Gauge Theories: The Causal Approach

TL;DR

This paper develops a rigorous, finite perturbative construction of Yang-Mills theories using the causal Epstein-Glaser method, avoiding regularization and clarifying gauge invariance and unitarity.

Contribution

It introduces a causal approach to nonabelian gauge theories that ensures finiteness, proves gauge invariance and unitarity without regularization, and separates infrared and ultraviolet issues.

Findings

Proves normalizability of Yang-Mills with fermions.

Establishes gauge invariance using free asymptotic fields.

Demonstrates physical unitarity of the S-matrix.

Abstract

We present the causal construction of perturbative Yang-Mills theories in four(3+1)-dimensional space-time. We work with free quantum fields throughout. The inductive causal method by Epstein and Glaser leads directly to a finite perturbation series and does not rely on an intermediary regularization of the theory. The causal method naturally separates the physical infrared problem of massless theories from ultraviolet-sensitive features like normalizability by regarding the distributional character of the S-matrix. We prove the normalizability of the Yang-Mills theory with fermionic matter fields and study the discrete symmetry transformations in the causal formalism. We introduce a definition of nonabelian gauge invariance which only involves the free asymptotic field operators and give mathematically rigorous and conceptually simple proofs of nonabelian gauge invariance and of the physical unitarity of the S-matrix in all orders of perturbation theory.