Hamiltonian Reduction in Affine Principal Bundles

TL;DR

This paper develops a Hamiltonian reduction method for field theories on affine principal bundles, providing a connection-free approach to describe reduced multisymplectic spaces and their dynamics.

Contribution

It introduces a canonical identification for Hamiltonian reduction in affine principal bundles, extending Lagrangian reduction theory to a Hamiltonian setting without using connections.

Findings

Derived the reduced Hamilton-Cartan equations.

Established a reduced covariant bracket for dynamics.

Applied the framework to molecular strands as an example.

Abstract

This paper presents a Hamiltonian reduction procedure for field theories over affine principal bundles introducing a canonical identification to describe the reduced multisymplectic space without the introduction of a connection. The main goal is to provide a Hamiltonian analogue of the Lagrangian reduction theory developed in M. Castrill\'on L\'opez, P. M. Chac\'on, and P. L. Garc\'ia. J. Geom. Mech., 5(4):399-414, 2013. The core of this work lies in the derivation of this canonical identification, the reduced Hamilton-Cartan equations, and a reduced covariant bracket that describes the dynamics. Finally, this theoretical framework is illustrated with a fundamental example: molecular strands.