Geodesics or autoparallels from a variational principle?
Abstract
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 nonholonomic frames we conclude that there is no reason to modify the conventional variational principle that leads to geodesics.
 Publication:

arXiv eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.grqc/9712013
 arXiv:
 arXiv:grqc/9712013
 Bibcode:
 1997gr.qc....12013S
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Latex, 13 pages, no figures