Singular symplectic cotangent bundle reduction of gauge field theory

We prove a theorem on singular symplectic cotangent bundle reduction in the Fréchet setting and apply it to Yang–Mills–Higgs theory with special emphasis on the Higgs sector of the Glashow–Weinberg–Salam model. For the latter model, we give a detailed description of the reduced phase space and show that the singular structure is encoded in a finite-dimensional Lie group action.