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Modern Physics Letters A

WEYL-ORDERED POLYNOMIALS STUDIED BY VIRTUE OF THE IWWOP TECHNIQUE

Hong-Yi Fan

Published Dec 21, 2000• 22 citations
Publisher

Abstract

We investigate the properties of the Weyl-ordered polynomials Tm,n by the technique of integration within a Weyl-ordered product (IWWOP) and the Weyl quantization rule. The introduction of the Weyl-ordering symbol ⋮⋮ and the IWWOP provide us with a convenient approach for deriving the Weyl-ordered form of the product of Tm,n and other operators. The Weyl-ordered Dirac's δ-function form of the Wigner operator can also directly lead us to the Weyl quantization formalism for the functions of radial vaiables.

DOI
10.1142/s0217732300001808

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Communications in Theoretical Physics•Oct 15, 2003•8 citations
We investigate the properties of the Weyl-ordered polynomials Tm,n by the technique of integration within a Weyl-ordered product (IWWOP) and the Weyl quantization rule. The introduction of the Weyl-ordering symbol ⋮⋮ and the IWWOP provide us with a convenient approach for deriving the Weyl-ordered form of the product of Tm,n and other operators. The Weyl-ordered Dirac's δ-function form of the Wigner operator can also directly lead us to the Weyl quantization formalism for the functions of radial vaiables.
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated.