Dirac's monopole, quaternions, and the Zassenhaus formula

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.

arXiv commentLaTeX, 19 pages; published version, minor typos corrected

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Cited by in corpus (9)

• Quaternionic electrodynamics
• Dirac's magnetic monopole and the Kontsevich star product
• Closed forms of the Zassenhaus formula
• The Kirillov picture for the Wigner particle
• Self-interacting quantum particles
• On the structure and convergence of the symmetric Zassenhaus formula
• Self-interacting quantum particles and the Dirac delta potential
• Quantum self-interaction within an infinitely deep cavity
• Generalized imaginary units in quantum mechanics