Auxiliary fields in the geometrical relativistic particle dynamics

TL;DR

This paper introduces an auxiliary variables method for modeling relativistic particle dynamics along timelike or null curves, simplifying higher-order derivative actions through constraints and a covariant formalism, with applications to particle models.

Contribution

It presents a novel auxiliary variables approach for relativistic particle dynamics, especially for null curves, reducing higher-order actions to lower order with constraints.

Findings

The method effectively simplifies higher-order derivative actions.

Application to null curves demonstrates the approach's versatility.

The formalism provides a covariant framework for particle models.

Abstract

We describe how to construct the dynamics of relativistic particles following, either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting physical particle models governed by actions that involve higher order derivatives of the embedding functions of the worldline. We point out that the mechanical content of such models can be extracted wisely from a lower order action, which can be performed by implementing in the action a finite number of constraints that involve the geometrical relationship structures inherent to a curve and by using a covariant formalism. We emphasize our approach for null curves. For such systems, the natural time parameter is a pseudo-arclength whose properties resemble those of the standard proper time. We illustrate the formalism by applying it to some models for relativistic particles.