Mathisson' spinning electron: noncommutative mechanics & exotic Galilean symmetry, 66 years ago
Abstract
The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's classical electron [Acta Physica Polonica 6, 218 (1937)], further discussed by Weyssenhoff and Raabe [Acta Physica Polonica 9, 7 (1947)]. The two-parameter centrally extended Galilean symmetry of the model is recoved using elementary methods. The relation to Schr\"odinger's Zitternde Elektron is indicated.
Keywords
Cite
@article{arxiv.hep-th/0303099,
title = {Mathisson' spinning electron: noncommutative mechanics & exotic Galilean symmetry, 66 years ago},
author = {P. A. Horvathy},
journal= {arXiv preprint arXiv:hep-th/0303099},
year = {2007}
}
Comments
Final version, published in Acta Physica Polonica 34, 2611 (2003). Dedicated to the memory of M. Mathisson, J. Weyssenhoff and A. Raabe, who tried to continue to do research during those terrible years of World War II. Revised version. The relation with Schr\"odinger's Zitternde Elektron indicated, and Dirac's Obituary on Mathisson is added. Latex, no figures. 9 pages