Integral form of Yang-Mills equations and its gauge invariant conserved charges

L. A. Ferreira and G. Luchini
Phys. Rev. D 86, 085039 – Published 26 October 2012

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 Yang-Mills equations and calculate the conserved charges associated with 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.

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  • Received 14 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.085039

© 2012 American Physical Society

Authors & Affiliations

L. A. Ferreira* and G. Luchini

  • Instituto de Física de São Carlos, IFSC/USP, Universidade de São Paulo—USP, Caixa Postal 369, CEP 13560-970, São Carlos-SP, Brazil

  • *laf@ifsc.usp.br
  • gabriel.luchini@gmail.com

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Issue

Vol. 86, Iss. 8 — 15 October 2012

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