A new approach to classical Einstein-Yang-Mills Theory

TL;DR

This paper introduces a novel Hamiltonian approach to Einstein-Yang-Mills theory, connecting gauge symmetries with Cartan's invariant integral and deriving generators as Noether charges, enhancing understanding of spacetime and gauge invariances.

Contribution

It presents a new Hamiltonian framework that unifies gauge and diffeomorphism symmetries in Einstein-Yang-Mills theory using Cartan's approach and Noether charges.

Findings

Hamiltonian generators are derived as vanishing Noether charges.

The approach links gauge symmetries with Cartan's invariant integral.

Provides a consistent interpretation of symmetry variations.

Abstract

The conventional Rosenfeld-Bergmann-Dirac constrained Hamiltonian algorithm applied to Einstein-Yang-Mills theory is shown to be equivalent to a local gauge theoretic extension of Cartan's invariant integral approach to classical mechanics. In addition, the Hamiltonian generators of Legendre-projectable spacetime diffeomorphism and gauge symmetries are derived directly as vanishing Noether charges. This leads directly to their interpretation as delivering the correct symmetry variations of both configuration and momentum feld variables.