Singular symplectic cotangent bundle reduction of gauge field theory

TL;DR

This paper develops a theorem for singular symplectic cotangent bundle reduction in infinite-dimensional Fréchet spaces and applies it to analyze the reduced phase space in gauge field theories like the Glashow-Weinberg-Salam model.

Contribution

It introduces a new theorem for singular symplectic reduction in the Fréchet setting and applies it to gauge theories, providing detailed descriptions of the reduced phase space.

Findings

Reduced phase space for Yang-Mills-Higgs theory characterized

Singular structure encoded in finite-dimensional Lie group action

Application to the Higgs sector of the Standard Model

Abstract

We prove a theorem on singular symplectic cotangent bundle reduction in the Fr\'echet 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.