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College Physics

Weyl prescription based on the anti-normal ordering technology

XU Shi-mi

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

Wigner operator and Weyl prescription are studied by virtue of the skill of differential-integral and the method of operators' differential quotient.The differential formula of Wigner operator in normal ordering is given,and new differential formulae of some special functions are obtained.It is more important that the integral divergent difficulty is smoothed away and the differential formula of Wigner operator and the Weyl prescription in anti-normal ordering are derived.Several examples are calculated.

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Wigner operator and Weyl prescription are studied by virtue of the skill of differential-integral and the method of operators' differential quotient.The differential formula of Wigner operator in normal ordering is given,and new differential formulae of some special functions are obtained.It is more important that the integral divergent difficulty is smoothed away and the differential formula of Wigner operator and the Weyl prescription in anti-normal ordering are derived.Several examples are calculated.
Differential quotient rule of composite function operator and its applications in quantum physics, quantum statistics, operator ordering theory, matrix theory and control theory are given. The integration problem of Wigner operator and Weyl corresponding rules are studied. Two kinds of typical operator identity formulas are proved. The differential form of Wigner operator in ordered product of operators and new differential form of important functions are obtained. Finally, a Wigner operator with parameter for unifying regular order, Weyl sequencing and abnormal order is introduced.
In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f ( λ + ν ) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.
We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner function's zero-point value is also discussed.