On the finiteness of the discrete spectrum of a 3x3 operator matrix
DOI:
Keywords:
Operator matrix, bosonic Fock space, annihilation and creation operators, generalized Friedrichs model, essential and discrete spectra, Weinberg equation, continuity in the uniform operator topologyAbstract
An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra of two families of the generalized Friedrichs models. A symmetric version of the Weinberg equation for eigenvectors of $H$ is obtained. The conditions which guarantee the finiteness of the number of discrete eigenvalues located below the bottom of the three-particle branch of the essential spectrum of $H$ is found.References
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