Fourier Duality as a Quantization Principle

Details Fourier Duality as a Quantization Principle Fourier Duality as a Quantization Principle

1996-08-27

arxiv.org/abs/funct-an/9608005v2

Int.J.Theor.Phys. 36 (1997) 345-383

Mathematics

Operator Algebras

LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 97Kb, 43 pages, no figures. requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final v

Scientific paper

10.1007/BF02435738

The Weyl-Wigner 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 non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner 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.

Affiliated with

Also associated with

No associations

Rating

Fourier Duality as a Quantization Principle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fourier Duality as a Quantization Principle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fourier Duality as a Quantization Principle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-696817