Dirac’s monopole, quaternions, and the Zassenhaus formula
Michael Alexandrovich Soloviev
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 $\ensuremath{\hbar}$. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.
arXiv:1608.04707•Physical review. D/Physical review. D.•Nov 23, 2016•9 citations