Poincare Cartan Form for Gauge Fields in Curved Background

TL;DR

This paper develops a covariant Hamiltonian framework for gauge fields in curved spacetime, modifying the Poincare-Cartan form to preserve gauge invariance with covariant derivatives.

Contribution

It introduces a covariant Hamiltonian formulation for gauge fields in curved backgrounds, extending the Poincare-Cartan form with covariant derivatives for gauge invariance.

Findings

Formulation maintains gauge invariance in curved spacetime

Poincare-Cartan forms are adapted with covariant derivatives

Framework applicable to differential 1-form gauge fields

Abstract

The `directly Hamiltonian' field theory in the extended phase space is applied to gauge fields in curved spacetime background. These fields being differential 1-forms, have canonical momenta which are 2-forms. The Poincare-Cartan 4-forms for matter and gauge fields have to be modified with the exterior derivatives replaced by the covariant derivative for maintaining gauge invariance.