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Chin. Phys. B, 2010, Vol. 19(5): 050303    DOI: 10.1088/1674-1056/19/5/050303
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Unifying the theory of integration within normal-, Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

Fan Hong-Yi(范洪义)
Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
Abstract  By introducing the $s$-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within $s$-ordered product of operators (which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases). The $s$-ordered operator expansion (denoted by $\circledS \cdots \circledS)$ formula of density operators is derived, which is $$\rho=\frac{2}{1-s}\int \frac{{\rm d}^2\beta}{\pi}\left \langle -\beta \right \vert \rho \left \vert \beta \right \rangle \circledS \exp \Big\{ \frac{2}{s-1}\left( s'\beta'^{2}-\beta^{\ast}a+\beta a^{\dagger}-a^{\dagger}a\right) \Big\} \circledS.$$ The $s$-parameterized quantization scheme is thus completely established.
Keywords:  s-parameterized generalized Wigner operator      technique of integration within s-ordered product of operators      s-ordered operator expansion formula      s-parameterized quantization scheme  
Received:  18 September 2009      Revised:  10 October 2009      Accepted manuscript online: 
PACS:  03.65.Vf (Phases: geometric; dynamic or topological)  
  02.30.Tb (Operator theory)  
  02.30.Cj (Measure and integration)  
  02.30.Mv (Approximations and expansions)  
  02.50.Ng (Distribution theory and Monte Carlo studies)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~10775097 and 10874174).

Cite this article: 

Fan Hong-Yi(范洪义) Unifying the theory of integration within normal-, Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators 2010 Chin. Phys. B 19 050303

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[1] s-parameterized Weyl transformation and the corresponding quantization scheme
Wang Ji-Suo (王继锁), Meng Xiang-Guo (孟祥国), Fan Hong-Yi (范洪义). Chin. Phys. B, 2015, 24(1): 014203.
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