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arXiv · quant-ph/0112110

Alternative commutation relations, star products and tomography

Olga V. Man'ko·V. I. Man'ko·G. Marmo
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Abstract

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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Olga V. Man'ko, V. I. Man'ko, G. Marmo. 2001-12-19. Alternative commutation relations, star products and tomography. https://doi.org/10.1088/0305-4470%2F35%2F3%2F315

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