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

Abstract

A gauge transformation provided by the three eigenfunctions of ${\text{B}}^a(x)\cdot {\text{B}}^b(x)$ (where ${\text{B}}^a(x)$, 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.

Comments: 12 pages; typos corrected, references added, other minor changes and additions