Abstract
We present a simpler and more powerful versionof the recently-discovered action principle for themotion of a spinless point particle in spacetimes withcurvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion witha torsion force, thus changing geodesics toautoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure ofparallelograms in the presence of torsion.
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Kleinert, H., Pelster, A. Letter: Autoparallels From a New Action Principle. General Relativity and Gravitation 31, 1439–1447 (1999). https://doi.org/10.1023/A:1026701613987
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DOI: https://doi.org/10.1023/A:1026701613987