Vacuum states from a resolution of the lightcone singularity

Abstract

The lightcone singularity at the origin is resolved by blowing up the singular point to CP 1. The Lorentz group acts on the resolved lightcone and has CP 1 as a special orbit. Using Wigner’s method of associating unitary irreducible representations of the Poincaré group to particle states, we find that the special orbit gives rise to new vacuum states. These vacuum states are labelled by the principal series representations of SL(2,C). Some remarks are included on the applications of these results to gauge theories and asymptotically flat spacetimes.