English

Geodesics or autoparallels from a variational principle?

General Relativity and Quantum Cosmology 2007-05-23 v1

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 non-holonomic frames we conclude that there is no reason to modify the conventional variational principle that leads to geodesics.

Keywords

Cite

@article{arxiv.gr-qc/9712013,
  title  = {Geodesics or autoparallels from a variational principle?},
  author = {Nuno Barros e Sa},
  journal= {arXiv preprint arXiv:gr-qc/9712013},
  year   = {2007}
}

Comments

Latex, 13 pages, no figures

R2 v1 2026-07-22T12:54:00.299Z