Stress-Energy-Momentum Tensors in Constraint Field Theories

TL;DR

This paper explores the complexities of defining the true energy-momentum tensor in constraint field theories, proposing a solution within the multimomentum Hamiltonian formalism, with applications to gauge theory and affine-metric gravity.

Contribution

It introduces a framework to select appropriate stress-energy-momentum tensors for different solutions in constraint field systems, clarifying their role in various theories.

Findings

Different solutions require different stress-energy-momentum tensors.

The multimomentum Hamiltonian formalism effectively addresses the tensor selection problem.

Application to gauge theory and affine-metric gravity demonstrates the framework's utility.

Abstract

One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum Hamiltonian formalism which provides the adequate description of constraint field systems. The goal is that, for different solutions of the same constraint field model, one should choose different stress-energy-momentum tensors in general. Gauge theory illustrates this result. The stress-energy-momentum tensors of affine-metric gravity are examined.