A geometrical analysis of the field equations in field theory

TL;DR

This paper reviews a geometric approach to classical field theory equations, exploring their solution existence, uniqueness, and integrability within Lagrangian and Hamiltonian frameworks using multivector fields.

Contribution

It introduces a geometric formulation of field equations in classical field theories, emphasizing the role of multivector fields in analyzing solutions.

Findings

Discusses existence and non-uniqueness of solutions.

Analyzes integrability conditions.

Provides a unified geometric framework.

Abstract

In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and non-uniqueness of solutions, as well as their integrability.