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

doi:10.1088/1674-1056/21/6/064204

中国物理B ›› 2012, Vol. 21 ›› Issue (6): 64204-064204.doi: 10.1088/1674-1056/21/6/064204

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

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

王继锁^{a b}, 范洪义^b, 孟祥国^{b c}

a. Shandong Provincial Key Laboratory of Laser Polarization and Information Technology,College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
b. Department of Physics, Liaocheng University, Liaocheng 252059, China;
c. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China

收稿日期:2011-11-18 修回日期:2011-12-10 出版日期:2012-05-01 发布日期:2012-05-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027), and the Program of Higher Educational Science and Technology of Shandong Province, China (Grant No. J10LA15).

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

Wang Ji-Suo(王继锁)^a)b)†, Fan Hong-Yi(范洪义)^c), and Meng Xiang-Guo(孟祥国)^b)c)

a. Shandong Provincial Key Laboratory of Laser Polarization and Information Technology,College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
b. Department of Physics, Liaocheng University, Liaocheng 252059, China;
c. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China

Received:2011-11-18 Revised:2011-12-10 Online:2012-05-01 Published:2012-05-01
Contact: Wang Ji-Suo E-mail:jswang@qfnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027), and the Program of Higher Educational Science and Technology of Shandong Province, China (Grant No. J10LA15).

摘要/Abstract

摘要： By extending the usual Wigner operator to the s-parameterized one as (1/4π²)∫_-∞^∞ dyduexp≤[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.

关键词: generalized Wigner operator, generalized operator ordering rule, bivariate normal distribution

Abstract: By extending the usual Wigner operator to the s-parameterized one as (1/4π²)∫_-∞^∞ dyduexp≤[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.

Key words: generalized Wigner operator, generalized operator ordering rule, bivariate normal distribution

中图分类号: (Quantum optics)

42.50.-p

03.65.-w (Quantum mechanics) 05.30.-d (Quantum statistical mechanics)

王继锁, 范洪义, 孟祥国. A generalized Weyl–Wigner quantization scheme unifying P–Q and Q–P ordering and Weyl ordering of operators[J]. 中国物理B, 2012, 21(6): 64204-064204.

Wang Ji-Suo(王继锁), Fan Hong-Yi(范洪义), and Meng Xiang-Guo(孟祥国) . A generalized Weyl–Wigner quantization scheme unifying P–Q and Q–P ordering and Weyl ordering of operators[J]. Chin. Phys. B, 2012, 21(6): 64204-064204.

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

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

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