General Computations Without Fixing the Gauge

TL;DR

This paper introduces a gauge-invariant method within the exact renormalization group framework to compute expectation values of gauge-invariant operators in SU(N) Yang-Mills theory, enabling calculations without fixing a gauge.

Contribution

It presents a new gauge-invariant formalism for computing operator expectation values in Yang-Mills theory, avoiding gauge fixing and simplifying continuum calculations.

Findings

Derived a simple expression for gauge-invariant operator expectation values.

Computed the O(g^2) correction to the Wilson loop without fixing gauge.

Validated the approach by reproducing standard results directly in the continuum.

Abstract

Within the framework of a manifestly gauge invariant exact renormalization group for SU(N) Yang-Mills, we derive a simple expression for the expectation value of an arbitrary gauge invariant operator. We illustrate the use of this formula by computing the O(g^2) correction to the rectangular, Euclidean Wilson loop with sides T >> L. The standard result is trivially obtained, directly in the continuum, for the first time without fixing the gauge. We comment on possible future applications of the formalism.