Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wehler, Joachim
Institution: Ludwig-Maximilians-Universität München
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167571786
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