Eugene Wigner and Translational Symmetries
Abstract
As Einstein's $E = mc^{2}$ unifies the energy-momentum relation for massive and massless particles, Wigner's little group unifies their internal space-time symmetries. It is pointed out that translational symmetries play essential roles both in formulating the problem, and in deriving the conclusions. The input translational symmetry is the space-time translation, and the output translational symmetry is built in the E(2)-like little group for massless particles. The translational degrees of freedom in this little group are gauge degrees of freedom. It should be noted that a number of condensed matter physicists played important supporting and supplementary roles in Wigner's unification of internal space-time symmetries of massive and massless particles.
- Publication:
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arXiv e-prints
- Pub Date:
- December 1996
- DOI:
- 10.48550/arXiv.cond-mat/9612057
- arXiv:
- arXiv:cond-mat/9612057
- Bibcode:
- 1996cond.mat.12057K
- Keywords:
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- Condensed Matter;
- High Energy Physics - Theory
- E-Print:
- 11 pages, LaTeX file, no figures