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Cliffordization, Spin and Fermionic Star Products

Allen C. Hirshfeld·Peter Henselder·Thomas Spernat
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Abstract

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a canonical quantization procedure for systems with either bosonic of fermionic degrees of freedom. We illustrate this procedure for a number a physical examples, including bosonic, fermionic and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.

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Allen C. Hirshfeld, Peter Henselder, Thomas Spernat. 2004-04-29. Cliffordization, Spin and Fermionic Star Products. https://doi.org/10.1016/j.aop.2004.06.008

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