Eugene Paul Wigner's Nobel Prize

In 1963, Eugene Paul Wigner was awarded the Nobel Prize in Physics for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles. There are no disputes about this statement. On the other hand, there still is a question of why the statement did not mention Wigner's 1939 paper on the Lorentz group, which was regarded by Wigner and many others as his most important contribution in physics. By many physicists, this paper was regarded as a mathematical exposition having nothing to do with physics. However, it has been more than one half century since 1963, and it is of interest to see what progress has been made toward understanding physical implications of this paper and its historical role in physics. Wigner in his 1963 paper defined the subgroups of the Lorentz group whose transformations do not change the four-momentum of a given particle, and he called them the little groups. Thus, Wigner's little groups are for internal space-time symmetries of particles in the Lorentz-covariant world. Indeed, this subgroup can explain the electron spin and spins of other massive particles. However, for massless particles, there was a gap between his little group and electromagnetic waves derivable Maxwell's equations. This gap was not completely removed until 1990. The purpose of this report is to review the stormy historical process in which this gap is cleared. It is concluded that Wigner's little groups indeed can be combined into one Lorentz-covariant formula which can dictate the symmetry of the internal space-time time symmetries of massive and massless particles in the Lorentz covariant world, just like Einstein's energy-momentum relation applicable to both slow and massless particles.