Cylindrical Group and Massless Particles

  • Y. S. Kim
  • E. P. Wigner
Part of the The Scientific Papers book series (WIGNER, volume A / 3)


It is shown that the representation of the E(2)-like little group for photons can be reduced to the coordinate transformation matrix of the cylindrical group, which describes movement of a point on a cylindrical surface. The cylindrical group is isomorphic to the two-dimensional Euclidean group. As in the case of E(2), the cylindrical group can be regarded as a contraction of the three-dimensional rotation group. It is pointed out that the E(2)-like little group is the Lorentz-boosted O(3)-like little group for massive particles in the infinite-momentum/zeromass limit. This limiting process is shown to be identical to that of the contraction of O (3) to the cylindrical group. Gauge transformations for free massless particles can thus be regarded as Lorentz-boosted rotations.


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© Springer-Verlag Berlin Heidelberg 1997

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  • Y. S. Kim
  • E. P. Wigner

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