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Examples of group contraction

  • Session VI — Symmetry Breaking Group contraction and Extension and Bifurcation
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Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 180))

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Abstract

Two limiting processes are applied to a model which may describe the relativistic quantum mechanical rotator.The first limiting process is defined by the contraction of the Poincaré group representation to the representation of the extended Galilei group (non-relativistic limit), and the second by the contraction of the deSitter group representation to the representation of the Poincaré group (elementary limit). In the elementary limit the model describes a relativistic elementary particle and in the non-relativistic limit it describes a non-relativistic rotator.

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References

  1. I. E. Segal, Duke Math. J. 18, 221 (1951).

    Google Scholar 

  2. E. Inönü, E. P. Wigner, Proc. N. A. S. 39, 510 (1953).

    Google Scholar 

  3. There is a third correspondence, which I shall not discuss here, but which is very helpful in constructing the model of the relativistic quantum rotator. This is the classical limit establishing the connection to the classical relativistic rotator models of Takabayashi4]; Mukunda, Biedenharn, van Dam 5]; Regge, Hanson.6]

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  4. A. Bohm, Quantum Mechanics, Ch. III, Springer-Verlag, New York (1979).

    Google Scholar 

  5. T. Takabayashi, Prog. Theor. Phys. Suppl. 67, 1 (1979), and references therein.

    Google Scholar 

  6. N. Mukunda, H. van Dam and L. C. Biedenharn, Phys. Rev. D28, 1938 (1980).

    Google Scholar 

  7. A. J. Hanson, T. Regge, Annals of Phys. 87, 498 (1974).

    Google Scholar 

  8. F. Rohrlich, Nucl. Phys. B112, 177 (1978)

    Google Scholar 

  9. H. S. Green, Aust. J. Phys. 29, 483 (1976)

    Google Scholar 

  10. L. P. Staunton, Phys. Rev. D13, 3269 (1976)

    Google Scholar 

  11. A. Bohm, Phys. Rev. 175, 1767 (1968)

    Google Scholar 

  12. H. Bacry, J. Math. Phys. 5, 109 (1964)

    Google Scholar 

  13. R. J. Finkelstein, Phys. Rev. 75, 1079 (1949)

    Google Scholar 

  14. H. S. Snyder, Phys. Rev. 71, 38 (1947).

    Google Scholar 

  15. H. C. Corben, “Classical and Quantum Theories of Spinning Particles,” Ch. 11.8, Holden Day Inc., 1968.

    Google Scholar 

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Authors and Affiliations

  1. Center for Particle Theory, The University of Texas at Austin, 78712, Austin, Texas

    A. Bohm & R. R. Aldinger

Authors
  1. A. Bohm
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  2. R. R. Aldinger
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Editor information

M. Serdaroğlu E. Ínönü

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© 1983 Springer-Verlag

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Bohm, A., Aldinger, R.R. (1983). Examples of group contraction. In: Serdaroğlu, M., Ínönü, E. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12291-5_59

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  • DOI: https://doi.org/10.1007/3-540-12291-5_59

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12291-3

  • Online ISBN: 978-3-540-39621-5

  • eBook Packages: Springer Book Archive

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