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dc.contributor.authorvan Suijlekom, Walter D.
dc.date.accessioned2024-12-20T10:45:42Z
dc.date.available2024-12-20T10:45:42Z
dc.date.issued2025
dc.identifierONIX_20241220_9783031591204_64
dc.identifier.urihttps://library.oapen.org/handle/20.500.12657/96144
dc.description.abstractThis 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.
dc.languageEnglish
dc.relation.ispartofseriesMathematical Physics Studies
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometry
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PH Physics::PHP Particle and high-energy physics
dc.subject.otherAbelian Gauge Theories
dc.subject.otherConnes' Reconstruction Theorem
dc.subject.otherCyclic Cohomology
dc.subject.otherK-theory of C* Algebras
dc.subject.otherLocal Index Formula
dc.subject.otherNon-abelian Gauge Theories
dc.subject.otherNon-commutative Geometry
dc.subject.otherNon-commutative Manifolds
dc.subject.otherUnitary and Morita Equivalence of Spectral Triples
dc.subject.otherYang–Mills Gauge Theory
dc.titleNoncommutative Geometry and Particle Physics
dc.typebook
oapen.identifier.doi10.1007/978-3-031-59120-4
oapen.relation.isPublishedBy6c6992af-b843-4f46-859c-f6e9998e40d5
oapen.relation.isFundedByda087c60-8432-4f58-b2dd-747fc1a60025
oapen.relation.isbn9783031591204
oapen.relation.isbn9783031591198
oapen.collectionDutch Research Council (NWO)
oapen.imprintSpringer Nature Switzerland
oapen.pages315
oapen.place.publicationCham
oapen.grant.number[...]


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