General approach to functional forms for the exponential quadratic operators in coordinate-momentum space

In a recent paper (Nieto M M 1996 Quantum Semiclass. Opt. 8 1061, quant-ph/9605032), the one-dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering the multidimensional exponential quadratic operator (EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single-mode and double-mode EQO through the squeezed operator and the time-displacement operator of the harmonic oscillator.