Vacuum states from a resolution of the lightcone singularity

TL;DR

This paper resolves the lightcone singularity by geometric blow-up, revealing new vacuum states associated with principal series representations, with implications for gauge theories and flat spacetime physics.

Contribution

It introduces a novel geometric resolution of the lightcone singularity that uncovers new vacuum states linked to principal series representations of the Lorentz group.

Findings

New vacuum states arise from the resolved lightcone's special orbit.

Vacuum states are labeled by principal series representations of SL(2,C).

Results have potential applications in gauge theories and asymptotically flat spacetimes.

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 Poincar\'e 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.