Abstract
A phase space approach to systems with both: classical degrees of freedom and purely quantum discrete ones is discussed. Formulas for the Stratonovich–Weyl quantizer and star product for such systems are proposed. The Wigner function, its properties and the time evolution are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kim, Y.S., Noz, M.E.: Phase-space picture of quantum mechanics – group theoretical approach. World Scientific Lecture Notes in Physics, vol. 40. World Scientific, River Edge (1991). MR 1254881
Plebański, J.F., Przanowski, M., Tosiek, J.: The Weyl-Wigner-Moyal formalism. II. The Moyal bracket. Acta Phys. Polon. B 27(9), 1961–1990 (1996). MR 1420253
Przanowski, M., Tosiek, J.: From the discrete Weyl-Wigner formalism for symmetric ordering to a number-phase Wigner function. J. Math. Phys. 58(10), 102106, 19 (2017). MR 3714658
Przanowski, M., Tosiek, J., Turrubiates, F.J.: The Weyl-Wigner-Moyal formalism on a discrete phase space. I. A Wigner function for a nonrelativistic particle with spin. Fortschr. Phys. 67, 1900080 (2019).
Tosiek, J., Przanowski, M.: Weyl-Wigner-Moyal formalism. I. Operator ordering. Acta Phys. Polon. B 26(11), 1703–1716 (1995). MR 1368486
Zachos, C.K., Fairlie, D.B., Curtright, T.L. (eds.): Quantum Mechanics in Phase Space: An Overview with Selected Papers. World Scientific Series in 20th Century Physics, vol. 34. World Scientific, Singapore (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Przanowski, M., Tosiek, J., Turrubiates, F.J. (2020). The Weyl–Wigner–Moyal Formalism on a Discrete Phase Space. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXVIII. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-53305-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-53305-2_20
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-53304-5
Online ISBN: 978-3-030-53305-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)