The quantum-mechanical inhomogeneous symplectic group

The structure of the quantum-mechanical inhomogeneous symplectic group ISp(2, C) in single boson mode is discussed and, in addition to its most common realization by quadratic combinations of the boson annihilation and creation operators, other nonlinear realizations are considered. The most basic disentanglement relations of the separation of squeezing (including rotation) and displacement operators are derived using a three-dimensional fundamental representation. The phase factors are determined using a special approach involving transformation of the inhomogeneous quadratic form in the boson operators to a central point together with special normal- and antinormal-ordering relations. In appendix B, the most basic formulae of operator disentanglement are collected together and special cases of the derived relations are considered.