New action principle for classical particle trajectories in spaces with torsion
für Theoretische Physik, Freie Universität Berlin,
Arnimallee 14, D-14195 Berlin, Germany
Accepted: 14 June 1996
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.
PACS: 03.20.+i – Classical mechanics of discrete systems: general mathematical aspects / 04.20.Fy – Canonical formalism, Lagrangians, and variational principles / 02.40.Ma – Global differential geometry
© EDP Sciences, 1996