Resolve the lightcone singularity and extend the SO(3,1)-action

Joachim Wehler

Resolve the lightcone singularity and extend the SO(3,1)-action

Algebraic Geometry 2026-05-19 v1

Authors: Joachim Wehler

Abstract

Papadopoulos showed in 2021: The action of the Lorentz group SO(3,1) on the lightcone of Minkowski space lifts to an SO(3,1)-action on the blow-up of the lightcone. From this, he draws conclusions regarding further hypothetical vacuum states in quantum field theories. The present note shows that the possbility to lift the SO(3,1)-action to the blow-up is a pure mathematical result. It does not depend on the context from physics, in particular it does not make use of the Dirac equation. Instead, it is a simple application of the blow-up theory from algebraic geometry. Lifting is possible because the group action is linear and the exceptional divisor of the blow-up is the projectivized tangent cone.

Cite

@article{arxiv.2607.02527,
  title  = {Resolve the lightcone singularity and extend the SO(3,1)-action},
  author = {Joachim Wehler},
  journal= {arXiv preprint arXiv:2607.02527},
  year   = {2026}
}

Comments

3 pages, no figures