Completely integrable N-body problems in three-dimension and their relativistic generalization

  • A. O. Barut
Represations Theory
Part of the Lecture Notes in Physics book series (LNP, volume 135)


Quantum Number Dynamical Group Relativistic Generalization Independent Particle Model Integrable Dynamical System 
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    For integrable many-body problems in one-dimension and related studies see P. D. Lax, Comm. Pure and Appl Math. 21, 467 (1968) F. Calogero, J. Math. Phys. 10,2197 (1969); 12,419 (1971); 15,1420 (1974); M. Toda, Progr. Theor. Phys. Suppl. 45,1974 (1970),J. Moser, Advances in Math. 16, 197 (1975), M. A. Olshanetsky, A. M. Perelomov, Invent. Math. 37,93 (1976), Lett. Math. Phys. 2, 7 1977); H. Airault, H. P. McKean, J. Moser, Comm. Pure and Appl. Math. 30, 95 (1977). B. Kostant, Advances in Math. 34, 195-338 (1980).MATHMathSciNetGoogle Scholar
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    V. I. Arnold, Proof of a Theorem of A. N. Kolmogorov on the invariance of quasi-periodic Motions under small perturbations of the Hamiltonian, Russian Math. Surveys 18, 9–36 (1963) J. Moser, Nachr. Akad. Wiss. Göttinger, Math-Phys. K1. II a, 1–20 (1962).MATHCrossRefGoogle Scholar
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    A. 0. Barut, Phys. Rev. 133, B839 (1964) A. 0. Barut and A. Bohm, Phys. Rev. 139, B1107 (1965)MathSciNetCrossRefGoogle Scholar
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    A. 0. Barut, Reports in Math. Phys. 11, 401 (1977)MATHMathSciNetCrossRefGoogle Scholar
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    H. Weyl, The Theory of Groups and Quantum Mechanics,(Dover, N.Y. 1950)Google Scholar
  6. (6).
    A. 0. Barut, in Non-compact Group in Particle Physics, Edit. Y. Chow, (W. A. Benjamin, N.Y. 1966) p. 1–22.Google Scholar
  7. (7).
    A. 0. Barut, in Groups, Systems and Many-Body Physics,(Edit. by P. Kramer and M. Dal Cin, Vieweg 1980), Ch. 6, p. 285–317.Google Scholar
  8. (8).
    cf. for example, A. 0. Barut and R. Raczka, Group Representations and Applications, Warsaw 1977.Google Scholar
  9. (9).
    R. Peterhop, Theory of Ionisation of Atoms by Electron Impact, Color. Ass. Univ. Press, Boulder, 1977.Google Scholar
  10. (10).
    A. 0. Barut and Y. Kitagawara, (to be published)Google Scholar

Copyright information

© Spriger-Verlag 1980

Authors and Affiliations

  • A. O. Barut
    • 1
  1. 1.Department of PhysicsThe University of ColoradoBoulder

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