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
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.
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