Geodesics or autoparallels from a variational principle?

Details Geodesics or autoparallels from a variational principle? Geodesics or autoparallels from a variational principle?

1997-12-02

arxiv.org/abs/gr-qc/9712013v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 13 pages, no figures

Scientific paper

Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. The purpose of this letter is to call attention to the problems that such attempts raise, namely the requirement of a more elaborate structure in order to formulate the variational principle and the lack of a Hamiltonian description for the autoparallel motion. Here is also raised the problem of how to generalize this proposed new principle to quantum mechanics and to field theory. Since all applications known of such a principle are equally well described in terms of geodesics in non-holonomic frames we conclude that there is no reason to modify the conventional variational principle that leads to geodesics.

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