The lightcone singularity at the origin is resolved by blowing up the singular point to CP1. The Lorentz group acts on the resolved lightcone and has CP1 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 labeled 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.
|Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
|Early online date
|19 Jul 2021
|Published - 10 Sept 2021