Star products: a group-theoretical point of view

Details Star products: a group-theoretical point of view Star products: a group-theoretical point of view

2009-02-18

arxiv.org/abs/0902.3101v2

J.Phys.A42:475210,2009

Physics

Mathematical Physics

42 pages; conclusions added; a few references added

Scientific paper

10.1088/1751-8113/42/47/475210

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.

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