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

Abstract

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 FaL2T3 over L2(T3) is investigated. The location of the essential spectrum of the model operator H is described by means of the spectrum of the Friedreich model h(p); p∈ T3. Moreover, for the resolvent of H, the Faddeev type system of integral equations is obtained.