O(2,1)-like little group for spacelike four-momenta and localized light waves in continuous media

Abstract

While a light wave travels in a nonvacuum medium with speed less than the speed of light in vacuum, its energy-momentum four-vector is spacelike. Thus the little group for this light wave is locally isomorphic to O(2,1). It is shown that the transformation of this little group produces observable effects on the light wave, in contrast to the case of the E(2)-like little group for photons in vacuum. It is also shown that the little group can be defined for a localized light wave consisting of a superposition of waves with different frequencies traveling in the same direction.