Concatenating Variational Principles and the Kinetic Stress-Energy-Momentum Tensor

TL;DR

This paper introduces a method to unify variational principles for interacting systems, demonstrated through a Klein-Gordon field and charged particle, leading to a new derivation of the kinetic stress-energy-momentum tensor.

Contribution

It presents a novel approach to combine variational principles over different bases into a single framework, enabling unified analysis of interacting physical systems.

Findings

Unified Lagrangian treatment for interacting systems.

Group-theoretic derivation of the kinetic stress-energy-momentum tensor.

Application to Klein-Gordon field and charged particle interaction.

Abstract

We show how to "concatenate" variational principles over different bases into one over a single base, thereby providing a unified Lagrangian treatment of interacting systems. As an example we study a Klein-Gordon field interacting with a mesically charged particle. We employ our method to give a novel group-theoretic derivation of the kinetic stress-energy-momentum tensor density corresponding to the particle.