Noncommutative Geometry and Particle Physics
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We t...
Đã lưu trong:
| Tác giả chính: | |
|---|---|
| Định dạng: | Online |
| Ngôn ngữ: | Tiếng Anh |
| Được phát hành: |
Springer Nature
2025
|
| Những chủ đề: | |
| Truy cập trực tuyến: | ONIX_20241220_9783031591204_64 |
| Các nhãn: |
Không có thẻ, Là người đầu tiên thẻ bản ghi này!
|
| _version_ | 1869530518153854976 |
|---|---|
| author | van Suijlekom, Walter D. |
| author_browse | van Suijlekom, Walter D. |
| author_facet | van Suijlekom, Walter D. |
| author_sort | van Suijlekom, Walter D. |
| collection | Directory of Open Access Books |
| description | This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model. The second edition of the book contains numerous additional sections and updates. More examples of noncommutative manifolds have been added to the first part to better illustrate the concept of a noncommutative spin manifold and to showcase some of the key results in the field, such as the local index formula. The second part now includes the complete noncommutative geometric description of particle physics models beyond the Standard Model. This addition is particularly significant given the developments and discoveries at the Large Hadron Collider at CERN over the last few years. Additionally, a chapter on the recent progress in formulating noncommutative quantum theory has been included. The book is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. |
| format | Online |
| id | doab-20.500.12854ir-150248 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1502482025-07-21T15:44:03Z Noncommutative Geometry and Particle Physics van Suijlekom, Walter D. Abelian Gauge Theories Connes' Reconstruction Theorem Cyclic Cohomology K-theory of C* Algebras Local Index Formula Non-abelian Gauge Theories Non-commutative Geometry Non-commutative Manifolds Unitary and Morita Equivalence of Spectral Triples Yang–Mills Gauge Theory thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model. The second edition of the book contains numerous additional sections and updates. More examples of noncommutative manifolds have been added to the first part to better illustrate the concept of a noncommutative spin manifold and to showcase some of the key results in the field, such as the local index formula. The second part now includes the complete noncommutative geometric description of particle physics models beyond the Standard Model. This addition is particularly significant given the developments and discoveries at the Large Hadron Collider at CERN over the last few years. Additionally, a chapter on the recent progress in formulating noncommutative quantum theory has been included. The book is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. 2025-01-22T13:53:35Z 2025-01-22T13:53:35Z 2024-12-20T10:45:42Z 2025 book ONIX_20241220_9783031591204_64 https://library.oapen.org/handle/20.500.12657/96144 9783031591204 9783031591198 https://directory.doabooks.org/handle/20.500.12854/150248 eng Mathematical Physics Studies open access image/jpeg n/a https://library.oapen.org/bitstream/20.500.12657/96144/1/9783031591204.pdf Springer Nature Springer Nature Switzerland 10.1007/978-3-031-59120-4 10.1007/978-3-031-59120-4 9fa3421d-f917-4153-b9ab-fc337c396b5a e0bd4373-4073-4641-9c13-774e2b3e6588 da087c60-8432-4f58-b2dd-747fc1a60025 9783031591204 9783031591198 Dutch Research Council (NWO) Springer Nature Switzerland 315 Cham [...] Nederlandse Organisatie voor Wetenschappelijk Onderzoek Netherlands Organisation for Scientific Research 10.13039/501100003246 open access |
| spellingShingle | Abelian Gauge Theories Connes' Reconstruction Theorem Cyclic Cohomology K-theory of C* Algebras Local Index Formula Non-abelian Gauge Theories Non-commutative Geometry Non-commutative Manifolds Unitary and Morita Equivalence of Spectral Triples Yang–Mills Gauge Theory thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics van Suijlekom, Walter D. Noncommutative Geometry and Particle Physics |
| title | Noncommutative Geometry and Particle Physics |
| title_full | Noncommutative Geometry and Particle Physics |
| title_fullStr | Noncommutative Geometry and Particle Physics |
| title_full_unstemmed | Noncommutative Geometry and Particle Physics |
| title_short | Noncommutative Geometry and Particle Physics |
| title_sort | noncommutative geometry and particle physics |
| topic | Abelian Gauge Theories Connes' Reconstruction Theorem Cyclic Cohomology K-theory of C* Algebras Local Index Formula Non-abelian Gauge Theories Non-commutative Geometry Non-commutative Manifolds Unitary and Morita Equivalence of Spectral Triples Yang–Mills Gauge Theory thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics |
| topic_facet | Abelian Gauge Theories Connes' Reconstruction Theorem Cyclic Cohomology K-theory of C* Algebras Local Index Formula Non-abelian Gauge Theories Non-commutative Geometry Non-commutative Manifolds Unitary and Morita Equivalence of Spectral Triples Yang–Mills Gauge Theory thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry thema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics |
| url | ONIX_20241220_9783031591204_64 |
| work_keys_str_mv | AT vansuijlekomwalterd noncommutativegeometryandparticlephysics |