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 $\hslash$. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.

• Received 22 August 2016

DOI:https://doi.org/10.1103/PhysRevD.94.105021