Mathisson' spinning electron: noncommutative mechanics & exotic Galilean symmetry, 66 years ago

TL;DR

This paper explores the noncommutative mechanics of Mathisson's classical electron, deriving it as a non-relativistic limit and revealing its exotic Galilean symmetry, connecting historical models with modern noncommutative physics.

Contribution

It derives the noncommutative electron model as a non-relativistic limit of Mathisson's classical electron and uncovers its two-parameter centrally extended Galilean symmetry.

Findings

Model derived as non-relativistic limit of Mathisson's electron

Revealed two-parameter Galilean symmetry

Connected to Schrödinger's Zitternde Elektron

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.