Loop Representation of Wigner’s Little Groups

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Date

2017-6-23

Author

Başkal, Sibel
Kim, Young S.
Noz, Marilyn E

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Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathematical forms for massive and for massless particles. However, it is shown possible to construct one unified representation using a graphical description. This graphical approach allows us to describe vividly parity, time reversal, and charge conjugation of the internal symmetry groups. As for the language of group theory, the two-by-two representation is used throughout the paper. While this two-by-two representation is for spin-1/2 particles, it is shown possible to construct the representations for spin-0 particles, spin-1 particles, as well as for higher-spin particles, for both massive and massless cases. It is shown also that the four-by-four Dirac matrices constitute a two-by-two representation of Wigner's little group.

Subject Keywords

Wigner's little groups, Lorentz group, Gauge transformations, Massless Particles, Photons; Invariance, Rotations, Spin

URI

https://hdl.handle.net/11511/51582

Journal

Symmetry

DOI

https://doi.org/10.3390/sym9070097

Collections

Department of Physics, Article

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Citation Formats

S. Başkal, Y. S. Kim, and M. E. Noz, “Loop Representation of Wigner’s Little Groups,” Symmetry, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51582.