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Squeezing Bogoliubov transformations on the infinite mode CCR-algebra. (English) Zbl 0904.46059
The improvement of the transmission rate in optimal communication technique generated an increasing interest in the study of the squeezed states of light. This paper presents a self-contained exposition of the connection between quadratic Hamiltonians, Bogoliubov transformation and symplectic transformations in the Fock representation, where all statements are proved and illustrated by examples. The structure of strongly continuous symplectic groups on arbitrary complex pre-Hilbert space is determined. For this end a general decomposition theorem for generally unbounded symplectic transformations on arbitrary one-boson test function space is given.

MSC:
46N50 Applications of functional analysis in quantum physics
81V80 Quantum optics
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