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Foundations of Physics

, Volume 23, Issue 2, pp 245–260 | Cite as

Mechanical models for Lorentz group representations

  • N. Mukunda
Part I. Invited Papers Dedicated To Asim Orhan Barut

Abstract

Simple classical mechanical models are constructed to help understand the natures of certain unitary representations of the Lorentz groupSO(3, 1) associated with its action on spacetime. In particular, different kinds of Principal Series unitary irreducible representations ofSO(3, 1) with positive or negative quadratic Casimir invariant are seen to correspond to bounded and unbounded motions, respectively, in the mechanical models.

Keywords

Group Representation Mechanical Model Irreducible Representation Unitary Representation Lorentz Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References and footnotes

  1. 1.
    For general discussions see, for instance: M. A. Naimark,Linear Representations of the Lorentz Group (Macmillan, New York, 1964); I. M. Gel'fand, R. A. Minlos, and Z. Ya. Shapiro,Representations of the Rotation and Lorentz Groups and Their Applications (Macmillan, New York, 1963).Google Scholar
  2. 2.
    E. Majorana,Nuovo Cimento 9, 335 (1932).Google Scholar
  3. 3.
    P. A. M. Dirac,Proc. R. Soc. London A 183, 284 (1945).Google Scholar
  4. 4.
    Harish-Chandra,Proc. R. Soc. London A 189, 372 (1947).Google Scholar
  5. 5.
    I. M. Gel'fand and M. A. Naimark,Izv. Akad. Nauk SSSR 11, 411 (1947).Google Scholar
  6. 7.
    See, for instance: I. S. Shapiro,Sov. Phys. Doklady 1, 91 (1956); Chou Kuang-chao and L. G. Zastavenko,Sov. Phys. JETP 8, 990 (1959); N. Mukunda,J. Math. Phys. 9, 532 (1968); A. Chakrabarti, M. Levy-Nahas, and R. Seneor,J. Math. Phys. 9, 1274 (1968); A. Chakrabarti,J. Math. Phys. 12, 1822 (1971); I. M. Gel'fand, M. I. Graev, and N. Ya Vilenkin,Generalized Functions (Academic Press, New York, 1966), Vol. 5, Chapters V and VI; B. Radhakrishnan and N. Mukunda,J. Math. Phys. 15, 477 (1974).Google Scholar
  7. 8.
    See, for instance: N. Mukunda, H. van Dam, and L. C. Biedenharn,Phys. Rev. D 22, 1938 (1980);Relativistic Models of Extended Hadrons Obeying a Mass-Spin Trajectory Constraint (Lecture Notes in Physics, Vol. 165) (Springer, Berlin, 1982).Google Scholar
  8. 9.
    E. C. G. Sudarshan and N. Mukunda,Classical Dynamics—A Modern Perspective (Wiley, New York, 1974), Chapter 9.Google Scholar
  9. 10.
    P. A. M. Dirac,Can. J. Math. 2, 129 (1950);Proc. R. Soc. London A 246, 326 (1958).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • N. Mukunda
    • 1
  1. 1.Centre for Theoretical Studies and Department of PhysicsIndian Institute of ScienceBangaloreIndia

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