Is Quantization of QCD Unique at the Non-Perturbative Level ?

TL;DR

This paper shows that QCD's topological susceptibility is zero at the nonperturbative level in covariant gauge, suggesting non-uniqueness of QCD and implications for the strong CP problem.

Contribution

It demonstrates the non-uniqueness of nonperturbative QCD in covariant gauge through two derivations and comparative analysis with the canonical formalism.

Findings

QCD in covariant gauge yields zero topological susceptibility.

QCD is not uniquely defined at the nonperturbative level.

Supports the trivial resolution of the strong CP problem in covariant gauge.

Abstract

We find that QCD in covariant gauge yields zero for the topological susceptibility, even at the nonperturbative level. The result is derived in two ways, one using translational invariance, and the other using the BRST Hamiltonian. Comparison with the canonical formalism suggests that QCD is not uniquely defined at the nonperturbative level. Supporting evidence is also provided in 1+1 dimensions. Our results imply that the strong CP problem admits a trivial resolution in covariant gauge, but obstacles remain for the U(1) problem.