Accounting for monopole configurations in Yang-Mills theory in three Euclidean dimensions

TL;DR

This paper explores how topological monopole configurations in three-dimensional Yang-Mills theory can be identified and incorporated into the functional measure, revealing their interactions with gauge fields and reformulating the partition function as a local field theory.

Contribution

It introduces a gauge transformation based on eigenfunctions of magnetic fields to expose monopoles and derives an equivalent local field theory including these topological configurations.

Findings

Monopoles interact with photons and massless vector bosons.

The monopole plasma's partition function is equivalent to a local scalar field theory.

Topological degrees of freedom are integrated with perturbation theory.

Abstract

A gauge transformation provided by the three eigenfunctions of $\B^a(x) \cdot \B^b(x)$ (where $\B^a(x)$, with a=1,2,3, are the non-Abelian magnetic fields) exposes the topological configurations of the Yang-Mills fields. In particular, it gives Dirac monopoles interacting with `photons' and massless charged vector bosons. A magnetic dipole field at each monopole corresponds to infinitesimal translation of the monopole, and provides the functional measure a la collective coordinates. The grand canonical partition function of the monopole plasma is exactly equivalent to a local field theory with certain scalar fields interacting with the Yang-Mills fields. This integrates topological degrees of freedom with perturbation theory.