Star products: a group-theoretical point of view

Abstract

Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show that for this (implicitly defined) star product explicit formulae can be provided. Two significant examples are studied in detail: the group of translations on phase space and the one-dimensional affine group. The study of the first example leads to the Groenewold-Moyal star product. In the second example, the link with wavelet analysis is clarified.

42 pages; conclusions added; a few references added

References in corpus (5)

• Discrete phase space based on finite fields
• Alternative commutation relations, star products and tomography
• Star products, duality and double Lie algebras
• Duality symmetry for star products
• Frame transforms, star products and quantum mechanics on phase space

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