Symmetries of the space of connections on a principal G-bundle and related symplectic structures

TL;DR

This paper explores the symmetries and symplectic structures of the cotangent bundle of a principal G-bundle, focusing on automorphisms, connections, and reduction procedures to understand their geometric properties.

Contribution

It introduces a detailed analysis of G-invariant symplectic structures on cotangent bundles related to automorphisms and connections, extending the understanding of symmetries in geometric mechanics.

Findings

Characterization of G-invariant symplectic structures on T*P

Relation between automorphisms of TP and symplectic structures

Application of Marsden-Weinstein reduction to these structures

Abstract

We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP covering the identity map of P and commuting with the action of TG on TP. The symplectic structures corresponding to connections on P(M,G) are also investigated. The Marsden-Weinstein reduction procedure for these symplectic structures is discussed.