Noncommutative Geometry of Gravity, Strings and Fields: A Panoramic Overview
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914181647695872 |
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| author | Szabo, Richard J. |
| author_facet | Szabo, Richard J. |
| contents | These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key mathematical approaches presented include operator algebras such as $C^*$-algebras, K-theory, spectral geometry, quantum groups, and deformation quantization. Physical application areas considered include string theory, quantum field theory, and the Standard Model, as well as certain condensed matter systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative Geometry of Gravity, Strings and Fields: A Panoramic Overview Szabo, Richard J. High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry Quantum Algebra These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key mathematical approaches presented include operator algebras such as $C^*$-algebras, K-theory, spectral geometry, quantum groups, and deformation quantization. Physical application areas considered include string theory, quantum field theory, and the Standard Model, as well as certain condensed matter systems. |
| title | Noncommutative Geometry of Gravity, Strings and Fields: A Panoramic Overview |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2511.22672 |