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