The Geometry of the solution space of first order Hamiltonian field theories II: non-Abelian gauge theories

TL;DR

This paper extends the geometric analysis of solution spaces in first order Hamiltonian field theories to non-Abelian gauge theories, establishing a Poisson bracket structure using coisotropic embedding techniques.

Contribution

It introduces a novel geometric framework for non-Abelian gauge theories within Hamiltonian field theory, building on previous work to define a Poisson structure on solutions.

Findings

Established a Poisson bracket structure for non-Abelian gauge theories

Applied coisotropic embedding theorem to gauge theories

Extended geometric solution space analysis to more complex theories

Abstract

We go on with the program started in the companion paper [CDI+] of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian field theories. The case of non-Abelian gauge theories is addressed by using a suitable version of the coisotropic embedding theorem.