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

doi:10.1088/1674-1056/19/5/050303

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).

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

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