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Advances in Mathematical Physics
Volume 2014, Article ID 943868, 10 pages
Research Article

The Faddeev Equation and the Essential Spectrum of a Model Operator Associated with the Hamiltonian of a Nonconserved Number of Particles

1Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, Malaysia
2Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia
3Academic Lyceum Number One Under Samarkand Institute of Economics and Service, 140104 Samarkand, Uzbekistan

Received 13 February 2014; Accepted 9 April 2014; Published 2 June 2014

Academic Editor: Pavel Kurasov

Copyright © 2014 Zahriddin Muminov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A model describing a truncated operator H (truncated with respect to the number of particles) and acting in the direct sum of zero-, one-, and two-particle subspaces of fermionic Fock space over is investigated. The location of the essential spectrum of the model operator H is described by means of the spectrum of the Friedreich model . Moreover, for the resolvent of H, the Faddeev type system of integral equations is obtained.