New action principle for classical particle trajectories in spaces with torsion

Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany

Received: 11 March 1996
Accepted: 14 June 1996

Abstract

To comply with recent developments of path integrals in spaces with curvature and torsion, we find the correct variational principle for classical trajectories of spinless point-particles in such spaces. Although the action depends only on the length, the trajectories are autoparallels (straightest lines) rather than geodesics (shortest lines), due to the effects of a torsion force arising from a geometric peculiarity of the variational procedure.