Models of relativistic particle with curvature and torsion revisited

TL;DR

This paper revisits models of relativistic particles with Lagrangians depending on curvature and torsion in three-dimensional space, explicitly determining the moduli spaces of trajectories and closed solitons.

Contribution

It provides a complete and explicit characterization of the moduli spaces of trajectories and closed solitons for these models in D=3 space forms.

Findings

Explicit moduli spaces of trajectories are determined.

Moduli subspaces of closed solitons in the three sphere are characterized.

The analysis enhances understanding of relativistic particle models with curvature and torsion.

Abstract

Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and explicitly determined using the Lancret program. The moduli subspaces of closed solitons in the three sphere are also determined.