Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-10-23
Int.J.Mod.Phys.A12:71-78,1997
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, LaTeX file, no figures; presented at the 2nd International Workshop on Classical and Quantum Integrable Systems: Alge
Scientific paper
10.1142/S0217751X97000098
Einstein's $E = mc^{2}$ unifies the momentum-energy relations for massive and massless particles. According to Wigner, the internal space-time symmetries of massive and massless particles are isomorphic to $O(3)$ and $E(2)$ respectively. According to Inonu and Wigner, $O(3)$ can be contracted to $E(2)$ in the large-radius limit. It is noted that the $O(3)$-like little group for massive particles can be contracted to the $E(2)$-like little group for massless particles in the limit of large momentum and/or small mass. It is thus shown that transverse rotational degrees of freedom for massive particles become contracted to gauge degrees of freedom for massless particles.
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