Geometrical particle models on 3D null curves

TL;DR

This paper investigates (2+1)-dimensional particle models based on null curves in Minkowski space, analyzing their solution spaces and geometric properties, extending previous work on light-like particle dynamics.

Contribution

It provides a comprehensive analysis of null curve-based particle models in 3D Minkowski space, including moduli space characterization and solutions beyond pseudo-arc length proportional actions.

Findings

Moduli spaces of solutions are fully characterized.

Solutions exist even when the action is not proportional to pseudo-arc length.

The models extend previous studies by Nersessian and Ramos.

Abstract

The simplest (2+1)-dimensional mechanical systems associated with light-like curves, already studied by Nersessian and Ramos, are reconsidered. The action is linear in the curvature of the particle path and the moduli spaces of solutions are completely exhibited in 3-dimensional Minkowski background, even when the action is not proportional to the pseudo-arc length of the trajectory.