A detailed analysis of and a general decomposition theorem for in general unbounded symplectic transformations on an arbitrary complex pre-Hilbert space (one–boson test function space) are given. The structure of strongly continuous symplectic groups on such spaces is determined. The connection between quadratic Hamiltonians, Bogoliubov transformations, and symplectic transformations is discussed in the Fock representation, and their relevance for squeezing operations in quantum optics is pointed out. The results for this rather general class of transformations are proved in a self-contained fashion.
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Honegger et al. (1996) studied this question.
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