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...
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| Main Author | |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
30.11.2018
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1812.00038 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Bizi, Nadir |
| Author_xml | – sequence: 1 givenname: Nadir surname: Bizi fullname: Bizi, Nadir |
| BackLink | https://doi.org/10.48550/arXiv.1812.00038$$DView paper in arXiv |
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| Snippet | The subject of this PhD thesis is noncommutative geometry - more specifically
spectral triples - and how it can be generalized to semi-Riemannian manifolds... |
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| SubjectTerms | Mathematics - Differential Geometry Mathematics - Mathematical Physics Mathematics - Operator Algebras Physics - High Energy Physics - Theory Physics - Mathematical Physics |
| Title | Thesis: Semi-Riemannian Noncommutative Geometry, Gauge Theory, and the Standard Model of Particle Physics |
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