Reformulating Yang-Mills theory in terms of local gauge invariant variables

TL;DR

This paper introduces a canonical transformation that reformulates Yang-Mills theory using local gauge-invariant variables, linking it to the phase space of general relativity and enabling local metric evolution.

Contribution

It presents a novel canonical transformation that expresses Yang-Mills theory in terms of local gauge-invariant variables, connecting it to gravitational phase space.

Findings

Established a direct relation between Yang-Mills and ADM variables.

Mapped 3+1 dimensional Yang-Mills to local metric evolution.

Provided a new framework for analyzing gauge theories in gravitational terms.

Abstract

An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of metrics on 3 manifolds.