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

摘要

A model describing a truncated operatorH(truncated with respect to the number of particles) and acting in the direct sum of zero-, one-, and two-particle subspaces of fermionic Fock spaceFaL2T3overL2(T3)is investigated. The location of the essential spectrum of the model operatorHis described by means of the spectrum of the Friedreich modelh(p); p∈ T3. Moreover, for the resolvent ofH, the Faddeev type system of integral equations is obtained.