New action principle for classical particle trajectories in spaces with torsion

P. Fiziev; H. Kleinert

doi:doi:10.1209/epl/i1996-00555-0

New action principle for classical particle trajectories in spaces with torsion DOI: 10.1209/epl/i1996-00555-0

Europhys. Lett, 35 (4), pp. 241-246 (1996)

New action principle for classical particle trajectories in spaces with torsion

P. Fiziev and H. Kleinert

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

(received 11 March 1996; accepted in final form 14 June 1996)

PACS. 03.20+i - Classical mechanics of discrete systems: general mathematical aspects.
PACS. 04.20Fy - Canonical formalism, Lagrangians, and variational principles.
PACS. 02.40Ma - Global differential geometry.

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.