Duality transformation for 3+1 dimensional Yang-Mills theory

TL;DR

This paper derives a dual formulation of 3+1 dimensional Yang-Mills theory as an SO(3) gauge theory, revealing a non-local, self-dual structure through a canonical transformation that preserves gauge constraints.

Contribution

It introduces a novel duality transformation for Yang-Mills theory, expressing it as a non-local SO(3) gauge theory with self-dual properties.

Findings

Dual form is an SO(3) gauge theory

Duality is realized as a canonical transformation

The dual theory is non-local and self-dual

Abstract

Dual form of 3+1 dimensional Yang-Mills theory is obtained as another SO(3) gauge theory. Duality transformation is realized as a canonical transformation. The The non-abelian Gauss law implies the corresponding Gauss law for the dual theory. The dual theory is non-local. There is a non-local version of Yang-Mills theory which is self dual.