2002/03/09 by H. Kleinert, Hagen Kleinert, Kleinert, Hagen
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Control and Dynamics of Mobile Robots #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0203029
Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/258
arxiv created 2002/03/09 · openalex publication_date 2002/03/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I explain the geometric basis for the recently-discovered nonholonomic mapping principle which permits deriving laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. As an important consequence, it yields a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force makes trajectories autoparallel rather than geodesic. Its geometric origin is the closure failure of parallelograms in the presence of torsion, A simple generalization of the mapping principle transforms path integrals from flat spacetimes to those with curvature and torsion, thus playing the role of a quantum equivalence principle, applicable at present only to spaces with gradient torsion.