Star products: a group-theoretical point of view
arXiv:0902.3101 · doi:10.1088/1751-8113/42/47/475210
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