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Eulerian parametrization of Wigner’s little groups and gauge transformations in terms of rotations in two-component spinors

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Special Relativity and Quantum Theory

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 33))

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Abstract

A set of rotations and Lorentz boosts is presented for studying the three-parameter little groups of the Poincaré group. This set constitutes a Lorentz generalization of the Euler angles for the description of classical rigid bodies. The concept of Lorentz-generalized Euler rotations is then extended to the parametrization of the E(2)-like little group and the O(2,1)-like little group for massless and imaginary-mass particles, respectively. It is shown that the E(2)-like little group for massless particles is a limiting case of the O(3)-like or O(2,1)-like little group. A detailed analysis is carried out for the two-component SL(2,c) spinors. It is shown that the gauge degrees of freedom associated with the translationlike transformation of the E(2)-like little group can be traced to the SL(2,c) spins that fail to align themselves to their respective momenta in the limit of large momentum and/or vanishing mass.

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Author information

Authors and Affiliations

  1. SASC Technologies, Inc., 5809 Annapolis Road, Hyattsville, Maryland, 20784, USA

    D. Han

  2. Department of Physics and Astronomy, University of Maryland, College Park, Maryland, 20742, USA

    Y. S. Kim

  3. Department of Physics, Kyungpook National University, 635, Daegu, Korea

    D. Son

Authors
  1. D. Han
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  2. Y. S. Kim
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  3. D. Son
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Editor information

Editors and Affiliations

  1. Department of Radiology, New York University, USA

    M. E. Noz

  2. Department of Physics and Astronomy, University of Maryland, USA

    Y. S. Kim

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© 1988 Kluwer Academic Publishers

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Han, D., Kim, Y.S., Son, D. (1988). Eulerian parametrization of Wigner’s little groups and gauge transformations in terms of rotations in two-component spinors. In: Noz, M.E., Kim, Y.S. (eds) Special Relativity and Quantum Theory. Fundamental Theories of Physics, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3051-3_34

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  • DOI: https://doi.org/10.1007/978-94-009-3051-3_34

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7872-6

  • Online ISBN: 978-94-009-3051-3

  • eBook Packages: Springer Book Archive

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