Integrability in theories with local U(1) gauge symmetry
Abstract:
Using a recently developed method, based on a generalization of the zero
curvature representation of Zakharov and Shabat, we study the integrability
structure in the Abelian Higgs model. It is
shown that the model contains integrable sectors, where integrability is
understood as the existence of infinitely many conserved currents. In
particular, a gauge invariant description of the weak and strong integrable
sectors is provided. The pertinent integrability conditions are given by a
U(1) generalization of the standard strong and weak constraints for models with
two dimensional target space. The Bogomolny sector is discussed, as well,
and we find that each Bogomolny configuration
supports infinitely many conserved currents. Finally, other models with
U(1) gauge symmetry are investigated.