Wigner function under changes of reference frames

Authors

  • J. Berra Montiel Facultad de Ciencias, UASLP
  • G. F. Torres del Castilo Instituto de Ciencias, BUAP

DOI:

https://doi.org/10.31349/RevMexFisE.71.030702

Keywords:

Wigner function, Phase space quantum mechanics, reference frames

Abstract

We investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed Wigner function in both position and momentum representations. To illustrate our results, we include some basic examples.

References

M. Moshinsky and T.H. Seligman, Canonical transformations to action and angle variables and their representations in quantum mechanics, Ann. Phys. 114 (1978) 243–272.

F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization I. Deformations of symplectic structures, Ann. Phys. 111 (1978) 61–110.

C. Zachos, Deformation Quantization: Quantum Mechanics lives and works in phase-space, Int. J. Mod. Phys. A 17 (2002) 297. arXiv:hep-th/0110114.

R.P. Rundle and M.J. Everitt, Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies, Adv. Quant. Tech. 4 (2021) 2100016.

M. Reed and B. Simon, Methods of Modern Mathematical Physics. Volume I: Functional Analysis, 2nd ed. (Academic, San Diego, 1980).

L.A. Takhtajan, Quantum Mechanics for Mathematicians, Graduate Studies in Mathematics Vol. 95 (American Mathematical Society, 2008).

J. Weinbub and D.K. Ferry, Recent advances in Wigner function approaches, Appl. Phys. Rev. 5 (2018) 041104.

T.L. Curtright, D.B. Fairlie and C.K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space (World Scientific, Singapore, 2014). http://doi.org/10.1142/8870.

G. F. Torres del Castillo and B.C. N´ajera Salazar, Transformation of a wavefunction under changes of reference frame, Rev. Mex. FÍs. 63 (2017) 185.

C.C. Gerry and P.L. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2004). https://doi.org/10.1017/CBO9780511791239.

F. Giacomini, E. Castro-Ruiz and C. Brukner, Quantum mechanics and the covariance of physical laws in quantum reference frames, Nat. Commun. 10 (2019) 1–13

Downloads

Published

2025-05-01

How to Cite

[1]
J. Berra Montiel and G. F. Torres del Castilo, “Wigner function under changes of reference frames”, Rev. Mex. Fís., vol. 71, no. 3 May-Jun, pp. 030702 1–, May 2025.

Issue

Vol. 71 No. 3 May-Jun (2025): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

License

Copyright (c) 2025 J. Berra Montiel, G. F. Torres del Castilo

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.