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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Authors: | Fan Hong-Yi |
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Institution: | Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China |
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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
$$\rho=\frac{2}{1-s}\int
\frac{\d^2\beta}{\pi}\left \langle -\beta \right \vert \rho \left
\vert \beta \right \rangle \circledS \exp \Big\{ \frac{2}{s-1}\left(
s|\beta|^{2}-\beta^{\ast}a+\beta a^{\dagger}-a^{\dagger}a\right) \Big\}
\circledS.$$
The $s$-parameterized quantization scheme is thus completely
established. |
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Keywords: | s-parameterized generalized
Wigner operator technique of integration within s-ordered product
of operators s-ordered operator expansion formula s-parameterized quantization scheme |
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