Hamiltonian formulation of non-Abelian gauge theory with surface terms: applications to the dyon solution

Abstract

A Hamiltonian formulation is presented to include long-ranged, topologically nontrivial asymptotic structure, such as the dyon. The variational principle and its implications are discussed; a dynamical treatment of boundary conditions requires the extension of the usual phase space of the non-Abelian gauge theory to include gauge parameters at spatial infinity. A detailed discussion of internal charge rotations is presented; various gauges are discussed. In terms of the well-defined action of surface integrals on canonical variables we formulate a criterion for the admissibility of gauge conditions within the Hamiltonian formulation. A detailed discussion and existence of the Coulomb gauge is presented. The Poincaré invariance of the theory is established.