R. Aldrovandi, L.A. Saeger
Projective Fourier Duality and Weyl Quantization
(98K, LaTeX 2.09 with NFSS or AMSLaTeX 1.1, requires subeqnarray.sty, 44pp)
ABSTRACT. 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 {\em
projective Kac algebras} are shown to provide, in close parallel to the
standard case, a new dual framework and a well-defined notion of {\em
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.