## Differential Geometry and Physics

*Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics, Tianjin, China, 20-26 August 2005*

**Author**: Mo-Lin Ge,Weiping Zhang

**Publisher:**World Scientific

**ISBN:**9812703772

**Category:**Mathematics

**Page:**522

**View:**933

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This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.

## Geometry and Physics

**Author**: Jürgen Jost

**Publisher:**Springer Science & Business Media

**ISBN:**9783642005411

**Category:**Mathematics

**Page:**217

**View:**7433

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"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.

## Geometry and Physics

**Author**: H. Pedersen,J. Andersen,J. Dupont,Andrew Swann

**Publisher:**CRC Press

**ISBN:**9780824797911

**Category:**Mathematics

**Page:**768

**View:**404

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"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."

## Discrete Integrable Geometry and Physics

**Author**: Alexander I. Bobenko,Ruedi Seiler

**Publisher:**Oxford University Press, USA

**ISBN:**9780198501602

**Category:**Mathematics

**Page:**370

**View:**743

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Recent interactions between the fields of geometry, classical and quantum dynamical systems, and visualization of geometric objects such as curves and surfaces have led to the observation that most concepts of surface theory and of the theory of integrable systems have natural discreteanalogues. These are characterized by the property that the corresponding difference equations are integrable, and has led in turn to some important applications in areas of condensed matter physics and quantum field theory, amongst others. The book combines the efforts of a distinguished team ofauthors from various fields in mathematics and physics in an effort to provide an overview of the subject. The mathematical concepts of discrete geometry and discrete integrable systems are firstly presented as fundamental and valuable theories in themselves. In the following part these concepts areput into the context of classical and quantum dynamics.

## The Geometry and Physics of Knots

**Author**: Michael Francis Atiyah

**Publisher:**Cambridge University Press

**ISBN:**9780521395540

**Category:**Mathematics

**Page:**78

**View:**2167

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Deals with an area of research that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

## Noncommutative Geometry and Physics

*Renormalisation, Motives, Index Theory*

**Author**: Alan L. Carey

**Publisher:**European Mathematical Society

**ISBN:**9783037190081

**Category:**Mathematics

**Page:**273

**View:**1203

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## Geometry, Topology and Physics, Second Edition

**Author**: Mikio Nakahara

**Publisher:**CRC Press

**ISBN:**9780750306065

**Category:**Mathematics

**Page:**596

**View:**1920

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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.

## The Orbit Method in Geometry and Physics

*In Honor of A.A. Kirillov*

**Author**: Christian Duval,Laurent Guieu,Valentin Ovsienko

**Publisher:**Springer Science & Business Media

**ISBN:**1461200296

**Category:**Mathematics

**Page:**474

**View:**1331

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The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

## Geometry and physics

*non-Newtonian forms of dynamics*

**Author**: Asim Orhan Barut

**Publisher:**Humanities Pr

**ISBN:**N.A

**Category:**Mathematics

**Page:**123

**View:**4650

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## Higher Structures in Geometry and Physics

*In Honor of Murray Gerstenhaber and Jim Stasheff*

**Author**: Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu

**Publisher:**Springer Science & Business Media

**ISBN:**9780817647353

**Category:**Mathematics

**Page:**362

**View:**7219

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This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.

## Geometry and Physics: Volume 1

*A Festschrift in Honour of Nigel Hitchin*

**Author**: Andrew Dancer,Jørgen Ellegaard Andersen,Oscar Garcia-Prada

**Publisher:**Oxford University Press, USA

**ISBN:**0198802013

**Category:**Mathematics

**Page:**400

**View:**3809

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Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

## Geometry and Physics of Branes

**Author**: U Bruzzo,V. Gorini,U. Moschella

**Publisher:**CRC Press

**ISBN:**1420034294

**Category:**Science

**Page:**282

**View:**5063

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Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theories, such as homological mirror symmetry and quantum cohomology. Geometry and Physics of Branes provides an introduction to current research in some of these different areas, both in physics and mathematics. The book opens with a lucid introduction to the basic aspects of branes in string theory. Topics covered in subsequent chapters include tachyon condensation, the geometry surrounding the Gopakumar-Vafa conjecture (a duality between the SU(N) Chern-Simons theory on S3 and a IIA string theory compactified on a Calabi-Yau 3-fold), two-dimensional conformal field theory on open and unoriented surfaces, and the development of a homology theory naturally attached to the deformations of vector bundles that should be relevant to the study of homological mirror symmetry.

## The Symbolic Universe

*Geometry and Physics 1890-1930*

**Author**: Jeremy Gray

**Publisher:**Oxford University Press on Demand

**ISBN:**9780198500889

**Category:**Mathematics

**Page:**289

**View:**8578

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With the development of the theory of relativity by Albert Einstein, physics underwent a revolution at the end of the 19th century. The boundaries of research were extended still further when in 1907-8 Minkowski applied geometrical ideas to this area of physics. This in turn opened the door to other researchers seeking to use non-Euclidean geometrical methods in relativity, and many notable mathematicians did so, Weyl in particular linking these ideas with broader philosophical issues inmathematics. The Symbolic Universe gives an overview of this exciting era, giving a full account for the first time of Minkowski's geometric reformulation of the theory of special relativity.

## Groupoids in Analysis, Geometry, and Physics

*AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis, Geometry, and Physics, June 20-24, 1999, University of Colorado, Boulder*

**Author**: Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis,Arlan Ramsay,Jean Renault,AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE ON G,Geometry Ams-Ims-Siam Joint Summer Research Conference on Groupoids I

**Publisher:**American Mathematical Soc.

**ISBN:**0821820427

**Category:**Mathematics

**Page:**192

**View:**8092

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Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. For example, a foliation is an equivalence relation and has another groupoid associated with it, called the holonomy groupoid. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy.More generally, the use of groupoids is very much related to various notions of orbit equivalence. The point of view that groupoids describe 'singular spaces' can be found in the work of A. Grothendieck and is prevalent in the non-commutative geometry of A. Connes. This book presents the proceedings from the Joint Summer Research Conference on 'Groupoids in Analysis, Geometry, and Physics' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.

## Noncommutative Geometry and Physics 2005

*Proceedings of the International Sendai-Beijing Joint Workshop : Sendai, Japan, 1-4 November 2005, Beijing, China, 7-10 November 2005*

**Author**: Ursula Carow-Watamura

**Publisher:**World Scientific

**ISBN:**9812704698

**Category:**Mathematics

**Page:**324

**View:**3051

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Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space?time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.

## Global Analysis

*Differential Forms in Analysis, Geometry, and Physics*

**Author**: Ilka Agricola,Thomas Friedrich

**Publisher:**American Mathematical Soc.

**ISBN:**0821829513

**Category:**Mathematics

**Page:**343

**View:**942

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This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.

## Multivariable Calculus with MATLAB®

*With Applications to Geometry and Physics*

**Author**: Ronald L. Lipsman,Jonathan M. Rosenberg

**Publisher:**Springer

**ISBN:**331965070X

**Category:**Mathematics

**Page:**276

**View:**9816

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This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.

## Elementary vector analysis

*with application to geometry and physics*

**Author**: Charles Ernest Weatherburn

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**184

**View:**925

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## Quantization, Geometry and Noncommutative Structures in Mathematics and Physics

**Author**: Alexander Cardona,Pedro Morales,Hernán Ocampo,Sylvie Paycha,Andrés F. Reyes Lega

**Publisher:**Springer

**ISBN:**3319654276

**Category:**Science

**Page:**341

**View:**7244

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This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.

## Hopf Algebras in Noncommutative Geometry and Physics

**Author**: Stefaan Caenepeel,Fred Van Oystaeyen

**Publisher:**CRC Press

**ISBN:**9780824757595

**Category:**Mathematics

**Page:**344

**View:**4997

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This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the classification theory of finite dimensional Hopf algebras, categorical aspects of Hopf algebras, and recent advances in the theory of corings and quasi-Hopf algebras. It provides examples and basic properties of corings and their comodules in relation to ring and Hopf algebra theory and analyzes entwining structures and Morita theory for corings.