 96388 R. Aldrovandi, L.A. Saeger
 Fourier Duality as a Quantization Principle
(93K, LaTeX 2.09 with NFSS or AMSLaTeX 1.1, requires subeqnarray.sty, 44pp)
Aug 27, 96

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The WeylWigner prescription for quantization on Euclidean phase spaces makes
essential use of Fourier duality. The extension of this property to more
general phase spaces requires the use of Kac algebras, which provide the
necessary background for the implementation of Fourier duality on general
locally compact groups. Kac algebras  and the duality they incorporate  are
consequently examined as candidates for a general quantization framework
extending the usual formalism. Using as a test case the simplest nontrivial
phase space, the halfplane, it is shown how the structures present in the
completeplane case must be modified. Traces, for example, must be replaced by
their noncommutative generalizations  weights  and the correspondence
embodied in the WeylWigner formalism is no more complete. Provided the
underlying algebraic structure is suitably adapted to each case, Fourier
duality is shown to be indeed a very powerful guide to the quantization of
general physical systems.
 Files:
96388.tex