Alternative commutation relations, star products and tomography

Details Alternative commutation relations, star products and tomography Alternative commutation relations, star products and tomography

2001-12-19

arxiv.org/abs/quant-ph/0112110v1

Physics

Quantum Physics

LATEX plus two style files, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/35/3/315

Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are discussed. The recently introduced symplectic tomography map of observables (tomograms) related to the Heisenberg-Weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c-number functions. The star-product for symbols of the quantum-observable for each one of the maps (including the tomographic map) and explicit relations among different star-products are obtained. Deformations of the Moyal star-product and alternative commutation relations are also considered.

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