The Weyl Operator and its Generalization

RL Hudson, Kalyanapuram Rangachari Parthasarathy

徐兴磊, 李洪奇, 范洪义

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator ?k(p,q) with a real k parameter and can unify the P–Q, Q–P, and Weyl ordering of operators in k = 1,-1, 0, respectively, we find the mutual transformations between δ(p- P)δ(q- Q), δ(q- Q)δ(p- P), and Ωk(p,q), which are, respectively, the integration kernels of the P–Q, Q–P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The P- and Q- ordered forms of Ωk(p,q) are also derived,which helps us to put the operators into their P- and Q- ordering, respectively.

Fan Hong-Yi

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl ordering operator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operator functions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship between normal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS.

Xing-Lei Xu, Hongqi Li, Hong-Yi Fan

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ω k ( p , q ) with a real k parameter and can unify the P—Q , Q—P , and Weyl ordering of operators in k = 1, − 1, 0, respectively, we find the mutual transformations between δ ( p — P ) δ ( q — Q ), δ ( q — Q ) δ ( p — P ), and Ω k ( p, q ), which are, respectively, the integration kernels of the P—Q , Q—P , and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The — and — ordered forms of Ω k ( p , q ) are also derived, which helps us to put the operators into their — and — ordering, respectively.

Shunlong Luo