Talk detail

Participant	Ferreira, Luiz Agostinho
Institution	Instituto de Física de São Carlos, IFSC/USP - Av. Trabalhador são-carlense, 400 - Pq. Arnold Schimidt - São Carlos, SP - - Brazil

Session	QG1	Accepted	Yes	Order	9	Time	17:10 - 17:30
Talk	Oral abstract	Title	Integral formulation of Yang-Mills theory on loop spaces
Co-authors	G. Luchini
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. In this talk we present the integral form of the classical Yang-Mills equations in the presence of sources, as well as of its self-dual sector, 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. The construction is based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. 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. We also present the integral formulation for integrable field theories in lower dimensions like Chern-Simons theory.