Paolo Aniello 2009 J. Phys. A: Math. Theor. 42 475210 doi:10.1088/1751-8113/42/47/475210
Paolo Aniello
Show affiliationsAdopting 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.
02.20.Qs General properties, structure, and representation of Lie groups
03.65.Ta Foundations of quantum mechanics; measurement theory
81P15 Quantum measurement theory
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
Issue 47 (27 November 2009)
Received 7 April 2009, in final form 11 September 2009
Published 6 November 2009
Paolo Aniello 2009 J. Phys. A: Math. Theor. 42 475210
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