2025/07/25 by Sebastián Alí Sacasa-Céspedes, Sacasa-Céspedes, Sebastián Alí · 1 voice
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Lorentz covariance #Minkowski space #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Quantum #Quantum field theory #Quantum gravity #Regularization (linguistics) #Renormalization #Spacetime #Topology (electrical circuits) #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.2508.00885
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/07/25 · arxiv published 2025/07/25 · arxiv updated 2025/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification via stereographic projection, singularities are reframed as boundary artifacts. The framework employs causal embeddings and the causality group to preserve Lorentz invariance and unitarity, while homotopy-equivalent defect structures guarantee regularization independence via Stokes-Poincaré duality. The Physical Equivalence Theorem shows that homotopy-equivalent schemes yield identical renormalized observables. Renormalization group flows are governed by Euler characteristics, and anomalies are resolved through cobordism and Chern character integrals. This approach unifies UV/IR duality, anomaly cancellation, and Osterwalder-Schrader reconstruction. Applications extend to AdS/CFT, PDEs, quantum simulators, and noncommutative geometry. Topological regularization replaces artificial cutoffs with intrinsic geometric mechanisms, positioning spacetime as a defect-entangled structure governed by topological invariants, with testable predictions in quantum materials.