On elimination of the Gribov ambiguity

TL;DR

This paper develops a gauge-invariant strong coupling expansion for Yang-Mills theory that avoids the Gribov ambiguity by restricting calculations to the norm of the S-matrix, ensuring gauge invariance at each perturbation order.

Contribution

It introduces a formalism for Yang-Mills theory that eliminates the Gribov ambiguity through a gauge-invariant strong coupling expansion with a novel restriction.

Findings

Formalism is free of Gribov ambiguity at all orders

Perturbation theory remains gauge invariant

Calculations are confined within the S-matrix norm

Abstract

We find a strong coupling expansion around the non-trivial extremum of the Yang-Mills action. It is shown that the developed formalism is the Gribov ambiguity free since each order of the developed perturbation theory is transparently gauge invariant. The success is a consequence of the restriction: calculations are not going beyond the norm of the $S$-matrix element.