Probability representation of quantum mechanics and star product quantization
Mar 19, 201914 pages
Part of Proceedings, Irreversible Processes in Nature and Technics : Moscow, Russia, January 29-31, 2019
Published in:
- J.Phys.Conf.Ser. 1348 (2019) 1, 012101
Contribution to:
- Published: Dec 20, 2019
e-Print:
- 1903.07932 [quant-ph]
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Abstract: (IOP)
This paper presents a review of star-product formalism. This formalism provides a description for quantum states and observables by means of the functions called’ symbols of operators’. Those functions are obtained via bijective maps of the operators acting in Hilbert space. Examples of the Wigner-Weyl symbols (Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified for the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators required for construction of bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relationship between structure constants of associative star-product of operator symbols and quantizer-dequantizer operators is reviewed.Note:
- send to Journal of Physics: Conference Series, based on the materials of the report at the X All-Russian Conference "Irreversible processes in nature and technology"
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