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

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.

arXiv comment12 pages; typos corrected, references added, other minor changes and additions

References in corpus (8)

• Feynman rules and beta-function for the BF Yang-Mills Theory
• Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement
• Gauge-independent Abelian mechanism of color confinement in gluodynamics
• Half-monopoles and half-vortices in the Yang-Mills theory
• Chiral zero-mode for abelian BPS dipoles
• A gauge-invariant mechanism for quark confinement and a new approach to the mass gap problem
• SU(2) Gauge Theory in Covariant (Maximal) Abelian Gauges
• Perturbation theory including topological degrees of freedom: Yang-Mills theory in three Euclidean dimensions