Star Products and Geometric Algebra

Details Star Products and Geometric Algebra Star Products and Geometric Algebra

2004-09-28

arxiv.org/abs/math-ph/0409073v1

Physics

Mathematical Physics

21 pages

Scientific paper

10.1016/j.aop.2004.09.020

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 coefficient part 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.

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