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

The subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be dedicated to the transition from Riemannian to sem...

Full description

Saved in:
Bibliographic Details
Main Author Bizi, Nadir
Format Journal Article
LanguageEnglish
Published 30.11.2018
Subjects
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Mathematics - Operator Algebras
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Online AccessGet full text
DOI10.48550/arxiv.1812.00038

Cover

More Information
Summary:The subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be dedicated to the transition from Riemannian to semi-Riemannian manifolds. This entails a study of Clifford algebras for indefinite vector spaces and Spin structures on semi-Riemannian manifolds. An important consequence of this is the introduction of Krein spaces, which will enable us to generalize spectral triples to indefinite spectral triples. In the second half of this thesis, we will apply the formalism of noncommutative differential forms to indefinite spectral triples to construct noncommutative gauge theories on Lorentzian spacetimes. We will then demonstrate how to recover the Standard Model.
DOI:10.48550/arxiv.1812.00038