Smooth Loops and Thomas Precession
General Physics
2013-05-01 v1
Abstract
Fundamentals of the local smooth loops due to Sabinin are concisely outlined together with the corresponding infinitesimal objects, so-called \nu-hyperalgebras, and the analogue of the Lie groups theory. We apply here this theory to to formulation of a new concept of loop of boosts. A quaternionic model of the three-parametric loop of boosts is obtained and a remarkable connection with geodesic loops of Lobachevskii space is found. A description of Thomas precession in the light of general theory of smooth loops is given.
Cite
@article{arxiv.1304.7763,
title = {Smooth Loops and Thomas Precession},
author = {Alexander I. Nesterov and Lev V. Sabinin},
journal= {arXiv preprint arXiv:1304.7763},
year = {2013}
}
Comments
19 pages