2024/03/26 by Daniel Spitz, Spitz, Daniel
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2403.17996
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On Lie algebra level the related conjugacy limits act isomorphically to concatenations of contractions. We axiomatically introduce projective quantum fields on homogeneous space-time geometries, based on correspondingly generalized unitary transformation behavior and projectivization of the field operators. Projective correlators and their expectation values remain well-defined in all geometry limits, which includes their ultraviolet and infrared limits. They can degenerate with support on space-time boundaries and other lower-dimensional space-time subspaces. We explore fermionic and bosonic superselection sectors as well as the irreducibility of projective quantum fields. Dirac fermions appear, which obey spin-statistics as composite quantum fields. The framework systematically formalizes and generalizes the ambient space techniques regularly employed in conformal field theory.