The integral equations of Yang-Mills and its gauge invariant conserved charges

Abstract

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources, and then use it to solve the long standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self dual Yangs-Mills equations, and calculate the conserved charges associated to them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-abelian gauge theories.

Version to appear in Physical Review D (46 pages, 3 figures, 1 table)

References in corpus (3)

• Integrable theories and loop spaces: fundamentals, applications and new developments
• Gauge and Integrable Theories in Loop Spaces
• On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

Cited by in corpus (9)

• Magnetic monopoles revisited: Models and searches at colliders and in the Cosmos
• A mild source for the Wu-Yang magnetic monopole
• A Generalised Self-Duality for the Yang-Mills-Higgs System
• A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges
• A direct test of the integral Yang-Mills equations through SU(2) monopoles
• Quantization due to the time evolution, with applications to Quantum Yang-Mills theory, Quantum Gravity and Classical Statistical Field Theory
• Relating the wave-function collapse with Euler's formula, with applications to Classical Statistical Field Theory
• Quantum Yang-Mills Charges in Strongly Coupled 2D Lattice QCD with Three Flavors
• A zero-curvature representation of electromagnetism and the conservation of electric charge