Energy-momentum tensors in classical field theories - a modern perspective

TL;DR

This paper introduces a modern geometric framework for energy-momentum tensors in classical field theories, emphasizing a Hilbert-type approach that simplifies proofs and offers new insights, especially in metric and metric-affine theories.

Contribution

It develops a unified geometric approach to energy-momentum tensors based on Hilbert-type definitions, enhancing simplicity and understanding in classical field theories.

Findings

Consistent with hypermomentum map definitions

Simplifies proofs of energy-momentum tensor properties

Provides new insights into metric and metric-affine theories

Abstract

The paper presents a general geometric approach to energy-momentum tensors in Lagrangian field theories, based on a Hilbert-type definition. The approach is consistent with the ones defining energy-momentum tensors in terms of hypermomentum maps given by the diffeomorphism invariance of the Lagrangian - and, in a sense, complementary to these, with the advantage of an increased simplicity of proofs and also, opening up new insights into the topic. A special attention is paid to the particular cases of metric and metric-affine theories.