Emergence of Lorentz symmetry from an almost-commutative twisted spectral triple

2025/02/25 by Gaston Nieuviarts, Nieuviarts, Gaston · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2502.18105

openalex publication_date 2025/02/25 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

This article demonstrates how the transition from a (Riemannian) twisted spectral triple to a pseudo-Riemannian spectral triple arises within an almost-commutative spectral triple. This opens a new perspective on the Lorentzian signature problem, showing that the almost-commutative structure at the heart of the noncommutative standard model of particle physics could be the origin of the emergence of a Lorentzian spectral triple, starting from self-adjoint Dirac operators and conventional inner product structures, in the framework of twisted spectral triples. We present an alternative to Wick rotation, acting on the metric and the Christoffel symbols in a way that does not introduce any complex numbers.

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• Emergence of Time from a Twisted Spectral Triple in Almost-Commutative Geometry

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• Thesis: Semi-Riemannian Noncommutative Geometry, Gauge Theory, and the Standard Model of Particle Physics