# Semi-riemannian noncommutative geometry, gauge theory, and the standard model of particle physics

@article{Bizi2018SemiriemannianNG, title={Semi-riemannian noncommutative geometry, gauge theory, and the standard model of particle physics}, author={Nadir Bizi}, journal={arXiv: Mathematical Physics}, year={2018} }

The subject of this thesis is noncommutative geometry - more specifically spectral triples - and how it can be used to unify General Relativity with the Standard Model of particle physics. This unification has already been achieved with spectral triples for Riemannian manifolds. The main concern of this thesis is to generalize this construction to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis will thus be dedicated to the transition… Expand

#### 9 Citations

Algebraic backgrounds for noncommutative Kaluza-Klein theory. I. Motivations and general framework

- Physics
- 2019

We investigate the representation of diffeomorphisms in Connes’ spectral triple formalism. By encoding the metric and spin structure in a moving frame, it is shown on the paradigmatic example of spin… Expand

Algebraic backgrounds: a framework for noncommutative Kaluza-Klein theory

- Physics, Mathematics
- 2019

We investigate the representation of diffeomorphisms in Connes' Spectral Triples formalism. By encoding the metric and spin structure in a moving frame, it is shown on the paradigmatic example of… Expand

Algebraic backgrounds for noncommutative Kaluza-Klein theory. II. The almost-commutative case and the standard model

- Physics
- 2019

We define almost-commutative algebraic backgrounds and give conditions on them allowing us to compute their configuration space in terms of those of the continuous and finite parts. We apply these… Expand

Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinors

- Mathematics, Physics
- Journal of Mathematical Physics
- 2019

We give examples illustrating the fact that the different space/time splittings of the tangent bundle of a semi-Riemannian spin manifold give rise to non-equivalent norms on the space of compactly… Expand

On the uniqueness of Barrett's solution to the fermion doubling problem in Noncommutative Geometry

- Physics, Mathematics
- 2019

A solution of the so-called fermion doubling problem in Connes' Noncommutative Standard Model has been given by Barrett in 2006 in the form of Majorana-Weyl conditions on the fermionic field. These… Expand

Spectral Noncommutative Geometry Standard Model and all that

- Physics, Mathematics
- International Journal of Modern Physics A
- 2019

We review the approach to the Standard Model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and… Expand

A U(1)B−L-extension of the standard model from noncommutative geometry

- Physics
- 2019

We derive a $U(1)_{B-L}$-extension of the Standard Model from a generalized Connes-Lott model with algebra ${\mathbb C}\oplus{\mathbb C}\oplus {\mathbb H}\oplus M_3({\mathbb C})$. This generalization… Expand

The geometry of physical observables

- Physics, Mathematics
- 2020

Jordan algebras were first introduced in an effort to restructure quantum mechanics purely in terms of physical observables. In this paper we explain why, if one attempts to reformulate the internal… Expand

The standard model, the Pati–Salam model, and ‘Jordan geometry’

- Physics, Mathematics
- 2019

We argue that the ordinary commutative-and-associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algebra (as in… Expand

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