The essential spectrum of relativistic multi-particle operators
Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 1, pp. 1-28.
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Lewis, Roger T.; Siedentop, Heinz; Vugalter, Simeon. The essential spectrum of relativistic multi-particle operators. Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 1, pp. 1-28. http://www.numdam.org/item/AIHPA_1997__67_1_1_0/

[1] S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-body Schrödinger Operators. Mathematical Notes 29. Princeton University Press, Princeton, 1 edition, 1982. | MR | Zbl

[2] E Balslev, Schrödinger operators with symmetries. Rep. Math. Phys., Vol. 5, 1974, pp. 219-280. | MR | Zbl

[3] E Balslev, Schrödinger operators with symmetries. II. Rep. Math. Phys., Vol. 5, 1974, pp. 393-413. | MR | Zbl

[4] H.L. Cycon, R.G. Froese, Werner Kirsch, and Barry Simon. Schrödinger Operators with Application to Quantum Mechanics and Global Geometry. Text and Monographs in Physics. Springer-Verlag, Berlin, 1 edition, 1987. | MR | Zbl

[5] W.D. Evans, R.T. Lewis and Y. Saitö, The Agmon spectral function for molecular hamiltonians with symmetry restrictions. Proc. Royal Soc. Lond. A, Vol. 440, 1993, pp. 621-638. | MR | Zbl

[6] W. Hunziker, On the spectra of Schrödinger multiparticle Hamiltonians. Helv. Phys. Acta, Vol. 39, 1966, pp. 451-462. | MR | Zbl

[7] K. Jörgens and J. Weidmann, Spectral Properties of Hamiltonian Operators, Vol. 313 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1 edition, 1973. | MR | Zbl

[8] E.H. Lieb, M. Loss, and H. Siedentop, Stability of Relativistic Matter via Thomas-Fermi Theory. Helv. Phys. Acta, In press. | MR | Zbl

[9] E.H. Lieb and Horng-Ter Yau, The stability and instability of relativistic matter. Commun. Math. Phys., Vol. 118, 1988, pp. 177-213. | MR | Zbl

[10] F.W.J. Olver, Bessel functions of integer order. In Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, chapter 9, pp. 355-433. Dover Publications, New York, 5 edition, 1968. | MR

[11] A. Persson, Bounds for the discrete spectrum of a semi-bounded Schrödinger operator. Math. Scand., Vol. 8, pp. 143-153, 1960. | MR | Zbl

[12] M. Reed and B. Simon, Methods of Modern Mathematical Physics, volume 4: Analysis of Operators. Academic Press, New York, 1 edition, 1978. | Zbl

[13] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton University Press, Princeton, New Jersey, 1 edition, 1971. | MR | Zbl

[ 14] B. Simon, Trace Ideals and Their Applications. Number 35 in London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1979. | MR | Zbl

[15] W. Thirring, Lehrbuch der Mathematischen Physik 3: Quantenmechanik von Atomen und Molekülen. Springer-Verlag, Wien, New York, 1 edition, 1979. | MR | Zbl

[16] C. Van Winter, Theory of finite systems of particles I. the Green function. Mat. Fys. Dan. Vid. Selsk., Vol. 2(8), 1964, pp. 1-60. | MR | Zbl

[17] S.A. Vugalter and G.M. Zhislin, On the finiteness of discrete spectrum in the n-particle problem. Rep. Math. Phys., Vol. 19(1), February 1984, pp. 39-90. | MR | Zbl

[18] G.M. Zislin, A study of the spectrum of the Schrödinger operator for a system of several particles. Trudy Moskov. Mat. Obsc., Vol. 9, 1960, pp. 81-120. | MR

[19] G.M. Zislin, Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a given symmetry. Mathematics of the USSR-Izvestija, Vol. 3(3), 1969, pp. 559-616. | Zbl