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Wigner rotations and little groups

Article

Abstract

Wigner’s little groups are the subgroups of the Poincaré group whose transformations leave the four-momentum of a given particle invariant. For a relativistic particle in motion the little group is a boosted rotation. On the other hand, the kinematical effect of two non-colinear Lorentz boosts is another boost preceded or follwed by a rotation, which is called the Wigner rotation. It is shown that there is always a Wigner rotation for a given little group rotation. The differences between those two rotations are clearly demonstrated and some interesting physical applications are presented.

Keywords

Wigner’s little groups Wigner rotations 

PACS

42.55.Ah 11.30.Cp 42.15.Eq 

References

  1. 1.
    L.H. Thomas, Nature (London) 117 (1926) 514.CrossRefADSGoogle Scholar
  2. 2.
    J.D. Jackson, Classical Electrodynamics, 3rd ed. Wiley, New York, 1999, pp. 552–553.MATHGoogle Scholar
  3. 3.
    E.P. Wigner, Ann. Math. 40 (1939) 149.CrossRefMathSciNetGoogle Scholar
  4. 4.
    E. Inönü and E.P. Wigner, Proc. Natl. Acad. Scie. (USA) 39 (1953) 510.MATHCrossRefADSGoogle Scholar
  5. 5.
    Y.S. Kim and E.P. Wigner, J. Math. Phys. 28 (1987) 1175; 31 (1990) 55.MATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    S. Ba§kal and Y.S. Kim, Phys. Rev. E 66 (2002) 26604.CrossRefADSGoogle Scholar
  7. 7.
    S. Ba§kal and Y.S. Kim, math-ph/0210056, to appear in Phys. Rev. E 67 (2003).Google Scholar
  8. 8.
    D. Han, Y.S. Kim Phys. Rev. A 37 (1988) 4494.CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Akadémiai Kiadó 2004

Authors and Affiliations

  1. 1.Department of PhysicsMiddle East Technical UniversityAnkaraTurkey

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