Quantization of Yang-Mills Theories without the Gribov Ambiguity

TL;DR

This paper introduces a new gauge condition for quantizing non-Abelian gauge theories on a specific manifold, eliminating the Gribov ambiguity and exhibiting behaviors similar to axial gauges in the ultraviolet region.

Contribution

The paper proposes a novel gauge condition that avoids the Gribov ambiguity for non-Abelian gauge theories on a toroidal manifold, with implications for perturbative analysis.

Findings

Perturbative calculations behave like axial gauge in ultraviolet.

Infrared behavior of the perturbative series is nontrivial.

The gauge condition is compatible with the manifold's boundary conditions.

Abstract

A gauge condition is presented here to quantize non-Abelian gauge theory on the manifold $R\otimes S^{1}\otimes S^{1}\otimes S^{1}$, which is free from the Gribov ambiguity. Perturbative calculations in the new gauge behave like the axial gauge in ultraviolet region, while infrared behaviours of the perturbative series are quite nontrivial. The new gauge condition, which reads $n\cdot\partial n\cdot A=0$, may not satisfy the requirement that $A^{\mu}(\infty)=0$ in conventional perturbative calculations. However, such contradiction is not harmful for gauge theories constructed on the manifold $R\otimes S^{1}\otimes S^{1}\otimes S^{1}$.