Dirac's monopole, quaternions, and the Zassenhaus formula
Mathematical Physics
2016-12-30 v2 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by the explicit calculation of the star product up to the second order in the Planck constant. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
Keywords
Cite
@article{arxiv.1608.04707,
title = {Dirac's monopole, quaternions, and the Zassenhaus formula},
author = {Michael A. Soloviev},
journal= {arXiv preprint arXiv:1608.04707},
year = {2016}
}
Comments
LaTeX, 19 pages; published version, minor typos corrected