Projective Fourier Duality and Weyl Quantization

Details Projective Fourier Duality and Weyl Quantization Projective Fourier Duality and Weyl Quantization

1996-08-27

arxiv.org/abs/funct-an/9608004v2

Int.J.Theor.Phys. 36 (1997) 573-612

Mathematics

Operator Algebras

LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 102Kb, 44 pages, no figures. requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final

Scientific paper

10.1007/BF02435880

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.

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