Speaker
Description
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. In this talk 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 non-abelian electric and magnetic conserved charges, for any field configuration, which are invariant under general gauge transformations. The construction is based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections, which resemble the techniques used in integrable field theories. The charges are explicitly evaluated
for monopoles and dyons. In the case of the Wu-Yang monopole the integral equations imply that such a solution needs a unique point source to be self-consistent. Our results
are important in the understanding of global properties of non-abelian gauge theories.
- L. A. Ferreira and G. Luchini, “Integral form of Yang-Mills equations and its gauge invariant conserved charges,” Phys. Rev. D 86 (2012), 085039;
doi:10.1103/PhysRevD.86.085039; [arXiv:1205.2088 [hep-th]] - L. A. Ferreira and G. Luchini, “Gauge and Integrable Theories in Loop Spaces,”
Nucl. Phys. B 858 (2012), 336-365;
doi:10.1016/j.nuclphysb.2012.01.005; [arXiv:1109.2606 [hep-th]].
