Star products and geometric algebra

Journal Article · Sun May 01 00:00:00 EDT 2005 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2004.09.020· OSTI ID:20690150

Henselder, Peter ^[1]; Hirshfeld, Allen C ^[1]; Spernat, Thomas ^[1]

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1. Fachbereich Physik, Universitaet Dortmund 44221, Dortmund (Germany)

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficients of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner.

• OSTI ID: 20690150
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 317; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CLASSICAL MECHANICS
CLIFFORD ALGEBRA
DEFORMATION
QUANTIZATION
QUANTUM MECHANICS
SPIN