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A class of noninvertible Bogoliubov transformations in an abstract Boson Fock space is used to construct in the Fock space a family of self-adjoint operators H which are quadratic in the annihilation and the creation operators and are of the form H=H0+HI with the property that the unperturbed part H0 may have embedded-eigenvalues unstable under the perturbation HI. Scattering theory associated with the pair (H0,H) is also discussed. In application to quantum field theory, the family of the operators H gives a unified description for the Hamiltonians of models of a quantum harmonic oscillator coupled to a quantized scalar or radiation field

Noninvertible Bogoliubov transformations and instability of embedded eigenvalues