中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50303-50303.doi: 10.1088/1674-1056/19/5/050303

• GENERAL • 上一篇    下一篇

Unifying the theory of integration within normal-, Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

范洪义   

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
  • 收稿日期:2009-09-18 修回日期:2009-10-10 出版日期:2010-05-15 发布日期:2010-05-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~10775097 and 10874174).

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)†   

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
  • Received:2009-09-18 Revised:2009-10-10 Online:2010-05-15 Published:2010-05-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~10775097 and 10874174).

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摘要： 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 $$\rho=\frac{2}{1-s}\int \frac{\d^2\beta}{\pi}\left \langle -\beta \right \vert \rho \left \vert \beta \right \rangle \circledS \exp \Big\{ \frac{2}{s-1}\left( s|\beta|^{2}-\beta^{\ast}a+\beta a^{\dagger}-a^{\dagger}a\right) \Big\} \circledS.$$ The $s$-parameterized quantization scheme is thus completely established.

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.

Key words: s-parameterized generalized Wigner operator, technique of integration within s-ordered product of operators, s-ordered operator expansion formula, s-parameterized quantization scheme

中图分类号:  (Phases: geometric; dynamic or topological)

  • 03.65.Vf
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)