The Wigner transform
[1], associates to every quantum operator
a real phase space function
, its symbol, via
Its inverse, the Weyl transformation
[2], gives a systematic way of associating quantum operators to classical distribution functions and is used in the Weyl quantization.
References:- [1]^ E.P. Wigner: On the quantum correction for thermodynamic equilibrium. In: Phys. Rev. 40, 1932, pp. 749–759.
- [2]^ H.Weyl , "Quantenmechanik und Gruppentheorie", Zeitschrift für Physik, 46 (1927) pp. 1–46