Noncommutative Geometry And Particle Physics

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Noncommutative Geometry and Particle Physics

Walter D. van Suijlekom
Noncommutative Geometry and Particle Physics Book PDF

Author : Walter D. van Suijlekom
Publisher : Springer
Page : 246 pages
File Size : 53,9 Mb
Release : 2014-07-21
Category : Science
ISBN : 9789401791625

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Noncommutative Geometry and Particle Physics by Walter D. van Suijlekom Pdf

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 and the Standard Model of Elementary Particle Physics

Florian Scheck,Wend Werner,Harald Upmeier
Noncommutative Geometry and the Standard Model of Elementary Particle Physics Book PDF

Author : Florian Scheck,Wend Werner,Harald Upmeier
Publisher : Springer
Page : 350 pages
File Size : 49,5 Mb
Release : 2008-01-11
Category : Science
ISBN : 9783540460824

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Noncommutative Geometry and the Standard Model of Elementary Particle Physics by Florian Scheck,Wend Werner,Harald Upmeier Pdf

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

Walter van Suijlekom
Noncommutative Geometry and Particle Physics Book PDF

Author : Walter van Suijlekom
Publisher : Springer
Page : 237 pages
File Size : 51,6 Mb
Release : 2014-07-27
Category : Science
ISBN : 9401791635

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Noncommutative Geometry and Particle Physics by Walter van Suijlekom Pdf

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.

Computational Science " ICCS 2002

Peter M. A. Sloot
Computational Science ICCS 2002 Book PDF

Author : Peter M. A. Sloot
Publisher : Unknown
Page : 0 pages
File Size : 55,5 Mb
Release : 2002
Category : Computational Mathematics and Numerical Analysis
ISBN : 8354046087

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Computational Science " ICCS 2002 by Peter M. A. Sloot Pdf

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, Quantum Fields and Motives

Alain Connes,Matilde Marcolli
Noncommutative Geometry Quantum Fields and Motives Book PDF

Author : Alain Connes,Matilde Marcolli
Publisher : American Mathematical Soc.
Page : 785 pages
File Size : 54,7 Mb
Release : 2019-03-13
Category : Electronic
ISBN : 9781470450458

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Noncommutative Geometry, Quantum Fields and Motives by Alain Connes,Matilde Marcolli Pdf

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

Supersymmetry and Noncommutative Geometry

Wim Beenakker,Thijs van den Broek,Walter D. Suijlekom
Supersymmetry and Noncommutative Geometry Book PDF

Author : Wim Beenakker,Thijs van den Broek,Walter D. Suijlekom
Publisher : Springer
Page : 137 pages
File Size : 45,6 Mb
Release : 2015-10-22
Category : Science
ISBN : 9783319247984

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Supersymmetry and Noncommutative Geometry by Wim Beenakker,Thijs van den Broek,Walter D. Suijlekom Pdf

In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far.The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model.This book is intended for mathematical/theoretical physicists with an interest in the applications of noncommutative geometry to supersymmetric field theories.

Advances in Noncommutative Geometry

Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu
Advances in Noncommutative Geometry Book PDF

Author : Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu
Publisher : Springer Nature
Page : 753 pages
File Size : 40,7 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 9783030295974

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Advances in Noncommutative Geometry by Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu Pdf

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes)

Gerhard Grensing
Structural Aspects Of Quantum Field Theory And Noncommutative Geometry Second Edition In 2 Volumes Book PDF

Author : Gerhard Grensing
Publisher : World Scientific
Page : 1656 pages
File Size : 45,6 Mb
Release : 2021-07-15
Category : Science
ISBN : 9789811237096

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Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) by Gerhard Grensing Pdf

The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on 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 second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.

Noncommutative Geometry

Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Noncommutative Geometry Book PDF

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 41,5 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540203575

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Noncommutative Geometry and the Standard Model of Elementary Particle Physics

Florian Scheck,Wend Werner,Harald Upmeier
Noncommutative Geometry and the Standard Model of Elementary Particle Physics Book PDF

Author : Florian Scheck,Wend Werner,Harald Upmeier
Publisher : Springer
Page : 350 pages
File Size : 54,8 Mb
Release : 2002-11-26
Category : Science
ISBN : 3540440712

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Noncommutative Geometry and the Standard Model of Elementary Particle Physics by Florian Scheck,Wend Werner,Harald Upmeier Pdf

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.

An Introduction to Noncommutative Geometry

Joseph C. Várilly
An Introduction to Noncommutative Geometry Book PDF

Author : Joseph C. Várilly
Publisher : European Mathematical Society
Page : 134 pages
File Size : 55,9 Mb
Release : 2006
Category : Mathematics
ISBN : 3037190248

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An Introduction to Noncommutative Geometry by Joseph C. Várilly Pdf

Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.

Noncommutative Structures in Mathematics and Physics

S. Duplij,Julius Wess
Noncommutative Structures in Mathematics and Physics Book PDF

Author : S. Duplij,Julius Wess
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401008365

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Noncommutative Structures in Mathematics and Physics by S. Duplij,Julius Wess Pdf

A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Structural Aspects of Quantum Field Theory and Noncommutative Geometry

Gerhard Grensing
Structural Aspects of Quantum Field Theory and Noncommutative Geometry Book PDF

Author : Gerhard Grensing
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 41,6 Mb
Release : 2013
Category : Noncommutative function spaces
ISBN : 9814472697

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Structural Aspects of Quantum Field Theory and Noncommutative Geometry by Gerhard Grensing Pdf

'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.

Spectral Action in Noncommutative Geometry

Michał Eckstein,Bruno Iochum
Spectral Action in Noncommutative Geometry Book PDF

Author : Michał Eckstein,Bruno Iochum
Publisher : Springer
Page : 155 pages
File Size : 51,9 Mb
Release : 2018-12-18
Category : Science
ISBN : 9783319947884

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Spectral Action in Noncommutative Geometry by Michał Eckstein,Bruno Iochum Pdf

What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.