# Momentum sections in Hamiltonian mechanics and sigma models

## TL;DR

This paper explores the structure of momentum sections within Hamiltonian systems and sigma models, extending the concept to higher-dimensional manifolds and connecting it with Hamiltonian Lie algebroid theory.

## Contribution

It introduces a generalization of momentum sections on pre-multisymplectic manifolds, linking Hamiltonian mechanics, sigma models, and Lie algebroid theory in a novel framework.

## Key findings

- Identifies a structure of momentum sections in constrained Hamiltonian systems and gauged sigma models.
- Proposes a higher-dimensional generalization of momentum sections on pre-multisymplectic manifolds.
- Connects Hamiltonian Lie algebroid theory with sigma models and multisymplectic geometry.

## Abstract

We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a pre-multisymplectic manifold by considering gauged sigma models on a higher dimensional manifold.