Rasulov, T. Kh. The Faddeev equation and the location of the essential spectrum of a model multi-particle operator. (English. Russian original) Zbl 1160.81016 Russ. Math. 52, No. 12, 50-59 (2008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 12, 59-69 (2008). Summary: In this paper we consider a model operator which acts in a three-particle cut subspace of the Fock space. We describe “two-particle” and “three-particle” branches of the essential spectrum and obtain an analog of the Faddeev equation for eigenfunctions of this operator. Cited in 6 Documents MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81S05 Commutation relations and statistics as related to quantum mechanics (general) 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:Fock space; model operator; essential spectrum; faddeev equation PDFBibTeX XMLCite \textit{T. Kh. Rasulov}, Russ. Math. 52, No. 12, 50--59 (2008; Zbl 1160.81016); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 12, 59--69 (2008) Full Text: DOI References: [1] D. Mattis, ”The Few-Body Problem on a Lattice,” Rev. Modern Phys. 58, 361–379 (1986). [2] K. O. Friedrichs, Perturbation of Spectra in Hilbert Space (Am. Math. Soc., Providence, 1965; Mir, Moscow, 1969). · Zbl 0142.11001 [3] V. A. Malyshev and R. A. Minlos, ”Cluster Operators,” Trudy seminara im. I. G. Petrovskogo, No. 9, 63–80 (1983). · Zbl 0531.47040 [4] R. A. Minlos and H. Spohn ”The Three-Body Problem in Radioactive Decay: the Case of One Atom and at Most Two Photons,” in Topics in Statistical and Theoretical Physics. Amer. Math. Soc. Transl. (2). Providence (R. I.): Amer. Math. Soc. 177, 159–193 (1996). · Zbl 0881.47049 [5] Yu. V. Zhukov and R. A. Minlos ”The Spectrum and Scattering in a ”Spin-Boson” Model with at Most Three Photons,” Teor. i Matem. Fizika 103(1), 63–81 (1995). [6] S. N. Lakaev and T. Kh. Rasulov, ”A Model in the Perturbation Theory for the Essential Spectra of Multi-Particle Operators,” Matem. Zametki 73(4), 556–564 (2003). [7] S. N. Lakaev and T. Kh. Rasulov, ”The Efimov Effect in theModel of the Perturbation Theory for the Essential Spectrum,” Funkts. Analiz i Ego Prilozh. 37(1), 81–84 (2003). [8] S. Albeverio, S. N. Lakaev, and T. H. Rasulov, ”On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics,” // J. Stat. Phys. 127(2), 191–220 (2006). · Zbl 1126.81022 [9] G. R. Edgorov and M. E. Muminov, ”The Spectrum of One Model Operator in Perturbation Theory for the Essential Spectrum,” Teor. i Matem. Fiz. 144(3), 544–554 (2005). [10] S. P. Merkur’ev and L. D. Faddeev, Quantum Scattering Theory for Multi-Particle Systems (Nauka, Leningrad, 1989) [in Russian]. [11] M. Reed and B. Simon, Methods of Modern Mathematical Physics. Analysis of Operators (Academic Press, New York, 1979; Mir, Moscow, 1982), Vol. 4. · Zbl 0405.47007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.