This article is cited in 4 papers

Discrete spectrum of a model operator in Fock space

T. H. Rasulov

A. Navoi Samarkand State University

Abstract: We consider a model describing a "truncated" operator (truncated with respect to the number of particles) acting in the direct sum of zero-, one-, and two-particle subspaces of a Fock space. Under some natural conditions on the parameters specifying the model, we prove that the discrete spectrum is finite.

Keywords: discrete spectrum, Fock space, compact operator, continuity in the uniform operator topology, Hilbert–Schmidt operator, Weinberg equation.

Received: 06.11.2006

DOI: 10.4213/tmf6107

 English version: Theoretical and Mathematical Physics, 2007, 152:3, 1313–1321

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