Projective fourier duality and Weyl quantization
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The Weyl-Wigner correspondence prescription, which makes great 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. Both an Abelian and a symmetricprojective Kac algebra are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion ofprojective 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.
KeywordsHeisenberg Group Central Extension Projective Representation Fourier Representation Weyl Quantization
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