A Family of Generalized Wigner Operators and Their Physical Meaning as Bivariate Normal Distribution
Ji‐Suo Wang, Xiang‐Guo Meng, Hong-Yi Fan · Chinese Physics Letters · 2011
By extending the usual Wigner operator to the s-parameterized one, we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P . This can be exposed by comparing the normally ordered form of Ω s with the standard form of the Gaussian bivariate normal distribution of random variables in statistics. Three different expressions of Ω s and the quantization scheme with use of it are presented.