Perturbation of embedded eigenvalues: A general class of exactly soluble models in Fock spaces (Q749841)

The author deals with perturbation problems of embedded eigenvalues for operators with infinite degrees of freedom acting in the tensor product of \(L^ 2({\mathbb{R}})\) and the Boson-Fock space over a Hilbert space. A general class of operators for which the problem is ``exactly soluble'' is constructed. If the Hilbert space is equal to \(L^ 2({\mathbb{R}}^ n)\), the class contains the Hamiltonians of standard models of a one- dimensional quantum harmonic oscillator coupled quadratically to a quantum scalar field on the \(n+1\)-dimensional space-time.