A Lorentzian version of the non-commutative geometry of the standard model of particle physics

Abstract

A formulation of the non-commutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian case is achieved by a modification of Connes' internal space geometry so that it has signature 6 (mod 8) rather than 0. The fermionic part of the Connes-Chamseddine spectral action can be formulated, and it is shown that it allows an extension with right-handed neutrinos and the correct mass terms for the see-saw mechanism of neutrino mass generation.

arXiv commentApprox. 14 pages. v2: minor corrections; conclusions unaffected

References in corpus (9)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Noncommutative Geometry and the standard model with neutrino mixing
• Classification of Finite Spectral Triples
• Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
• The standard model in noncommutative geometry and fermion doubling
• Can (noncommutative) geometry accommodate leptoquarks?
• Fermion masses in noncommutative geometry
• Non-commutative geometry and the standard model vacuum

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