New Action Principle for Classical Particle Trajectories in Spaces with Torsion

TL;DR

This paper establishes a new variational principle for classical particle trajectories in spaces with torsion, showing that trajectories are autoparallels influenced by a torsion force, extending the understanding of path integrals in such geometries.

Contribution

It introduces a novel action principle that correctly describes particle trajectories as autoparallels in spaces with torsion, differing from traditional geodesic-based approaches.

Findings

Trajectories are autoparallels, not geodesics, in spaces with torsion.

The action depends solely on the length but accounts for torsion effects.

A new torsion force influences particle paths, aligning with recent developments in path integrals.

Abstract

To comply with recent developments of path integrals in spaces with curvature and torsion we find the correct variational principle for the classical trajectories. Although the action depends only on the length, the trajectories are {\em autoparallels} rather than geodesics due to the effects of a new torsion force.