Probability representation of quantum mechanics and star product quantization

Mar 19, 2019
14 pages
Published in:
  • J.Phys.Conf.Ser. 1348 (2019) 1, 012101
  • Published: Dec 20, 2019
e-Print:

Citations per year

202020212022202331
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"