an:04173701
Zbl 0713.47010
Arai, Asao
Perturbation of embedded eigenvalues: A general class of exactly soluble models in Fock spaces
EN
Hokkaido Math. J. 19, No. 1, 1-34 (1990).
00174457
1990
j
47A55 47A70 47L90 81T15 47N50
Boson-Fock space over a Hilbert space; one-dimensional quantum harmonic oscillator coupled quadratically to a quantum scalar field
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.
S.D.Karakozov