Torsion and Lorentz symmetry from Twisted Spectral Triples

2024/01/15 by Pierre Martinetti, Martinetti, Pierre, Gaston Nieuviarts +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2401.07848

openalex publication_date 2024/01/15 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28

Abstract

By twisting the spectral triple of a riemannian spin manifold, we show how to generate an orthogonal and geodesic preserving torsion from a torsionless Dirac operator. We identify the group of twisted unitaries as the generator of torsion with co-exact three form. Through the fermionic action, the torsion term identifies with a Lorentzian energy-momentum 4-vector. The Lorentz group turns out to be a normal subgroup of the twisted unitaries. We also investigate the spectral action related to this model.

Cited by

• Emergence of Time from a Twisted Spectral Triple in Almost-Commutative Geometry
• The noncommutative residue, divergence theorems and the spectral geometry functional

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