Abstract

Date: 2015-10-07; view: 614.

Star products and geometric algebra

Peter Henselder , Allen C. Hirshfeld ^, and Thomas Spernat

Fachbereich Physik, Universität Dortmund 44221, Dortmund, Germany

Received 10 August 2004; accepted 20 September 2004. Available online 1 February 2005.

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.

PACS:03.65; 03.40.D; 03.65.F
Keywords:Star products; Geometric algebra; Deformation quantization