Killing Tensors and Conserved Quantities of a Relativistic Particle in External Fields

TL;DR

This paper extends Killing equations to relativistic particles under external forces, introducing generalized equations with a hierarchical structure, including conformal Killing equations, to identify conserved quantities.

Contribution

It presents a novel generalization of Killing equations for particles influenced by external fields, incorporating reparametrization invariance and hierarchical structures.

Findings

Derived generalized Killing equations for external force systems

Established hierarchical structure including conformal Killing equations

Provided framework for conserved quantities in relativistic particle dynamics

Abstract

We generalize Killing equations to a test particle system which is subjected to external force. We relax the conservation condition by virtue of reparametrization invariance of a particle orbit. As a result, we obtain generalized Killing equations which have hierarchical structure on the top of which a conformal Killing equation exists.