Noncommutative Geometry and the Standard Model of Elementary Particle Physics

Noncommutative Geometry and the Standard Model of Elementary Particle Physics
Title Noncommutative Geometry and the Standard Model of Elementary Particle Physics PDF eBook
Author Florian Scheck
Publisher Springer Science & Business Media
Pages 352
Release 2002-11-26
Genre Science
ISBN 3540440712

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The outcome of a close collaboration between mathematicians and mathematical physicists, these Lecture Notes present the foundations of A. Connes noncommutative geometry, as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.

Noncommutative Geometry and Particle Physics

Noncommutative Geometry and Particle Physics
Title Noncommutative Geometry and Particle Physics PDF eBook
Author Walter D. van Suijlekom
Publisher Springer
Pages 246
Release 2014-07-21
Genre Science
ISBN 9401791627

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This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It 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. 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.

Noncommutative Geometry, Quantum Fields and Motives

Noncommutative Geometry, Quantum Fields and Motives
Title Noncommutative Geometry, Quantum Fields and Motives PDF eBook
Author Alain Connes
Publisher American Mathematical Soc.
Pages 816
Release
Genre Mathematics
ISBN 9780821874783

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Noncommutative Geometry and the Standard Model of Elementary Particle Physics

Noncommutative Geometry and the Standard Model of Elementary Particle Physics
Title Noncommutative Geometry and the Standard Model of Elementary Particle Physics PDF eBook
Author Florian Scheck
Publisher Springer
Pages 352
Release 2008-01-11
Genre Science
ISBN 3540460829

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The outcome of a close collaboration between mathematicians and mathematical physicists, these lecture notes present the foundations of A. Connes noncommutative geometry as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.

Noncommutative Geometry and the Standard Model of Particle Physics

Noncommutative Geometry and the Standard Model of Particle Physics
Title Noncommutative Geometry and the Standard Model of Particle Physics PDF eBook
Author Christoph Alexander Stephan
Publisher
Pages 89
Release 2005
Genre
ISBN

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Alain Connes a découvert une approche algébrique à la géométrie en remplaçant la géométrie Riemannienne de spin ordinaire par des triplets spectraux. Un triplet spectral est un ensemble avec trois membres : une algèbre, un opérateur de Dirac et un espace de Hilbert. Toutes les informations géométriques de la variété sont codées dans les triplets spectraux. Une qualité nouvelle de cette reformulation est la possibilité d'inclure des espaces non commutatifs. Ils sont représentés par des algèbres non commutatives, alors que les espaces ordinaires sont codés par des algèbres commutatives. Il est maintenant possible de rendre les algèbres commutatives, qui représentent l'espace-temps, un petit peu non commutatives, en prenant le produit tensoriel avec une somme d'algèbres matricielles. Alain Connes et Ali Chamseddine ont découvert que, pour un certain choix d'algèbre matricielle, on obtient la relativité générale et la théorie de champ classique du modèle standard de la physique des particules. Les géométries presque-commutatifs offrent aussi une interprétation naturelle pour le boson de Higgs comme connexion dans la partie non commutative de la géométrie. Chaque triplet spectral presque-commutatif représente un modèle de Yang-Mills-Higgs et peut être un canditat potentiel pour une théorie physique. Dans cette thèse doctorale des restrictions physiques supplémentaires seront imposées sur les triplets spectraux, par exemple que les masses des fermions soient non-dégénérées et que la théorie soir renormalisable. A partir de ces principes fondamentaux tous les triplets spectraux presque-commutatifs ont été classifiés en collaboration avec les professeurs Thomas Schücker et Bruno Iochum, et avec Jan-Hendrik Jureit. Il est surprenant que le modèle standard de la physique des particules occupe une position proéminente dans cette classification. La question de savoir s'il y a des modèles physiques avec plus de quatre algèbres reste ouverte.

Computational Science " ICCS 2002

Computational Science
Title Computational Science " ICCS 2002 PDF eBook
Author Peter M. A. Sloot
Publisher
Pages 0
Release 2002
Genre Computational Mathematics and Numerical Analysis
ISBN 9788354046080

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The outcome of a close collaboration between mathematicians and mathematical physicists, these lecture notes present the foundations of A. Connes noncommutative geometry as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.

Structural Aspects Of Quantum Field Theory (In 2 Volumes)

Structural Aspects Of Quantum Field Theory (In 2 Volumes)
Title Structural Aspects Of Quantum Field Theory (In 2 Volumes) PDF eBook
Author Gerhard Grensing
Publisher World Scientific
Pages 1596
Release 2013-05-21
Genre Science
ISBN 9814472719

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'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.