$\mathfrak{Q}$ -, $\mathfrak{P}$ -, and Weyl-ordering of Squeezing Operators: New Operator Identities and Applications

Abstract

The basic operator ordering regarding to coordinate-momentum operator is discussed by virtue of the technique of integration within \(\mathfrak{Q}\)-ordering (all Q are on the left of all P) and \(\mathfrak{P}\)-ordering (all P are on the left of all Q). We derive new operator-ordering identities about \(\mathfrak{Q}\)-ordering , \(\mathfrak{P}\)-ordering and Weyl-ordering of both single-mode and two-mode squeezing operators. Its application in combinatorics is pointed out.