3+1 dimensional Yang-Mills theory as a local theory of evolution of metrics on 3 manifolds

TL;DR

This paper establishes a canonical transformation linking 3+1 dimensional Yang-Mills theory to the local evolution of metrics on 3-manifolds, bridging gauge theory and geometric evolution.

Contribution

It introduces an explicit canonical transformation connecting Yang-Mills theory to ADM variables, providing a new geometric perspective.

Findings

Maps Yang-Mills to metric evolution on 3-manifolds

Provides a canonical transformation explicitly

Bridges gauge theory with geometric evolution

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.