Non-Uniqueness of Quantized Yang-Mills Theories

TL;DR

This paper investigates the non-uniqueness in quantized Yang-Mills theories within the causal perturbation framework, revealing ambiguities in gauge-invariant couplings and their implications for higher-order gauge invariance.

Contribution

It demonstrates the existence of a two-parameter ambiguity in the ghost sector and analyzes the gauge invariance of these ambiguities at higher orders in the Epstein-Glaser approach.

Findings

Higher-order gauge invariance holds with added couplings.

Ambiguities are limited to divergence terms on the physical subspace.

The simplest theory excludes divergence- and coboundary-couplings.

Abstract

We consider quantized Yang-Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most general coupling which is gauge invariant in first order contains a two-parametric ambiguity in the ghost sector - a divergence- and a coboundary-coupling may be added. We prove (not completely) that the higher orders with these two additional couplings are gauge invariant, too. Moreover we show that the ambiguities of the n-point distributions restricted to the physical subspace are only a sum of divergences (in the sense of vector analysis). It turns out that the theory without divergence- and coboundary-coupling is the most simple one in a quite technical sense. The proofs for the n-point distributions containing coboundary-couplings are given up to third or fourth order only, whereas the statements about the divergence-coupling are proven in all orders.