# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1812.04707