1 research outputs found
Projective Fourier Duality and Weyl Quantization
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.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 102Kb, 44 pages, no figures.
requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with text
improvements and crucial typos correction