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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 |
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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.
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Received: 18 November 2011
Revised: 10 December 2011
Accepted manuscript online:
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PACS:
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42.50.-p
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(Quantum optics)
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03.65.-w
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(Quantum mechanics)
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05.30.-d
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(Quantum statistical mechanics)
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| Fund: 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). |
Corresponding Authors:
Wang Ji-Suo
E-mail: jswang@qfnu.edu.cn
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Cite this article:
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 2012 Chin. Phys. B 21 064204
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