Finite Pseudo-Riemannian Spectral Triples and The Standard Model

Abstract

Starting from the formulation of pseudo-Riemannian generalisation of real spectral triples we develop the data of geometries over finite-dimensional algebras with indefinite metric and their Riemannian parts. We then discuss the Standard Model spectral triple in this formalism and interpret the physical symmetry preserving the lepton number as a shadow of a finite pseudo-Riemannian structure.

arXiv comment15 pages, PACS 02.40.Gh, 12.60.-i, 11.30.Er

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Cited by in corpus (7)

• Spectral Noncommutative Geometry, Standard Model and all that
• A spectral geometry for the Standard Model without the fermion doubling
• On stability of Friedmann-Lemaître-Robertson-Walker solutions in doubled geometries
• Algebraic backgrounds: a framework for noncommutative Kaluza-Klein theory
• Pseudo-Riemannian Structures in Pati-Salam models
• Spectral action and the electroweak $\theta$-terms for the Standard Model without fermion doubling
• A critical survey of twisted spectral triples beyond the Standard Model