On the Multimomentum Bundles and the Legendre Maps in Field Theories

TL;DR

This paper explores the geometric structures underlying the Hamiltonian formalism in classical field theories, comparing various multimomentum bundles and their Legendre maps to clarify the concepts of regularity.

Contribution

It provides a comprehensive analysis and comparison of different multimomentum bundles and Legendre maps, extending the definitions of regular and almost-regular Lagrangian systems.

Findings

Comparison of multimomentum bundles and their canonical structures

Introduction and analysis of Legendre maps in the context of field theories

Extension of the concepts of regular and almost-regular Lagrangian systems

Abstract

We study the geometrical background of the Hamiltonian formalism of first-order Classical Field Theories. In particular, different proposals of multimomentum bundles existing in the usual literature (including their canonical structures) are analyzed and compared. The corresponding Legendre maps are introduced. As a consequence, the definition of regular and almost-regular Lagrangian systems is reviewed and extended from different but equivalent ways.