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Author | : Neculai S. Teleman |
Publisher | : Springer Nature |
Total Pages | : 398 |
Release | : 2019-11-10 |
Genre | : Mathematics |
ISBN | : 3030284336 |
Download From Differential Geometry to Non-commutative Geometry and Topology Book in PDF, ePub and Kindle
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Author | : Alain Connes |
Publisher | : Springer |
Total Pages | : 364 |
Release | : 2003-12-15 |
Genre | : Mathematics |
ISBN | : 3540397027 |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
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.
Author | : J. Madore |
Publisher | : Cambridge University Press |
Total Pages | : 381 |
Release | : 1999-06-24 |
Genre | : Mathematics |
ISBN | : 0521659914 |
Download An Introduction to Noncommutative Differential Geometry and Its Physical Applications Book in PDF, ePub and Kindle
A thoroughly revised introduction to non-commutative geometry.
Author | : G. Giachetta |
Publisher | : World Scientific |
Total Pages | : 716 |
Release | : 2005 |
Genre | : Science |
ISBN | : 9812561293 |
Download Geometric and Algebraic Topological Methods in Quantum Mechanics Book in PDF, ePub and Kindle
- The book collects all the advanced methods of quantization in the last decade. - It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.
Author | : Jose M. Gracia-Bondia |
Publisher | : Springer Science & Business Media |
Total Pages | : 692 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1461200059 |
Download Elements of Noncommutative Geometry Book in PDF, ePub and Kindle
Author | : Walter D. van Suijlekom |
Publisher | : Springer |
Total Pages | : 246 |
Release | : 2014-07-21 |
Genre | : Science |
ISBN | : 9401791627 |
Download Noncommutative Geometry and Particle Physics Book in PDF, ePub and Kindle
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.
Author | : Mikio Nakahara |
Publisher | : Taylor & Francis |
Total Pages | : 596 |
Release | : 2018-10-03 |
Genre | : Mathematics |
ISBN | : 1420056948 |
Download Geometry, Topology and Physics Book in PDF, ePub and Kindle
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Author | : Yoshiaki Maeda |
Publisher | : Springer Science & Business Media |
Total Pages | : 328 |
Release | : 2001-03-31 |
Genre | : Science |
ISBN | : 9780792369301 |
Download Noncommutative Differential Geometry and Its Applications to Physics Book in PDF, ePub and Kindle
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.
Author | : Alain Connes |
Publisher | : Gulf Professional Publishing |
Total Pages | : 678 |
Release | : 1994-11-22 |
Genre | : Mathematics |
ISBN | : 012185860X |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. First full treatment of the subject and its applications Written by the pioneer of this field Broad applications in mathematics Of interest across most fields Ideal as an introduction and survey Examples treated include: the space of Penrose tilings the space of leaves of a foliation the space of irreducible unitary representations of a discrete group the phase space in quantum mechanics the Brillouin zone in the quantum Hall effect A model of space time
Author | : Igor V. Nikolaev |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 292 |
Release | : 2022-07-18 |
Genre | : Mathematics |
ISBN | : 3110788810 |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.