A generalized Weyl-Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

作者：Wang Ji-Suo^*; Fan Hong-Yi; Meng Xiang-Guo

来源：Chinese Physics B, 2012, 21(6): 064204.

DOI：10.1088/1674-1056/21/6/064204

• generalized Wigner operator
• generalized operator ordering rule
• bivariate normal distribution

extending the usual Wigner operator to the s-parameterized one as
1/4 pi(2) integral(infinity)(-infinity) dydu exp [iu (q - Q) + iy (p -P) + i s/2 yu]
with s being a real parameter, we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule. This rule recovers P-Q ordering, Q-P ordering, and Weyl ordering of operators in s = 1, -1, 0 respectively. Hence it differs from the Cahill-Glaubers' ordering rule which unifies normal ordering, anti-normal ordering, and Weyl ordering. We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P. The formula that can rearrange a given operator into its new s-parameterized ordering is presented.

• 出版日期2012-6
• 单位上海交通大学; 曲阜师范大学; 聊城大学