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2009 J. Phys. A: Math. Theor. 42 475210 (29pp) doi: 10.1088/1751-8113/42/47/475210
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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 formulas 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.
PACS numbers: 03.65.Ca, 03.65.Ta, 03.65.Wj, 03.65.Fd, 02.20.Qs
Print publication: Issue 47 (27 November 2009) |
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