Thesis: SemiRiemannian Noncommutative Geometry, Gauge Theory, and the Standard Model of Particle Physics
Abstract
The subject of this PhD thesis is noncommutative geometry  more specifically spectral triples  and how it can be generalized to semiRiemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be dedicated to the transition from Riemannian to semiRiemannian manifolds. This entails a study of Clifford algebras for indefinite vector spaces and Spin structures on semiRiemannian 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1812.00038
 Bibcode:
 2018arXiv181200038B
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 Mathematics  Operator Algebras
 EPrint:
 180 pages, PhD thesis