Nonabelian Gauge Symmetry in the Causal Epstein-Glaser Approach

TL;DR

This paper extends the causal Epstein-Glaser approach to nonabelian gauge theories, establishing gauge invariance via a commutator relation and deriving the most general couplings consistent with unitarity and normalizability.

Contribution

It introduces a linear condition for nonabelian gauge invariance in the Epstein-Glaser framework and derives the resulting general couplings, including four-gluon and four-ghost interactions.

Findings

Nonabelian gauge invariance is defined by a simple commutator relation.

The most general couplings compatible with gauge invariance are derived.

Quadrilinear terms like four-gluon and four-ghost couplings are generated by the linear gauge invariance condition.

Abstract

We present some generalizations of a recently proposed alternative approach to nonabelian gauge theories based on the causal Epstein-Glaser method in perturbative quantum field theory. Nonabelian gauge invariance is defined by a simple commutator relation in every order of perturbation theory separately using only the linear (abelian) BRS-transformations of the asymptotic fields. This condition is sufficient for the unitarity of the S-matrix in the physical subspace. We derive the most general specific coupling compatible with the conditions of nonabelian gauge invariance and normalizability. We explicitly show that the quadrilinear terms, the four-gluon-coupling and the four-ghost-coupling, are generated by our linear condition of nonabelian gauge invariance. Moreover, we work out the required generalizations for linear gauges.