Geometry and Physics

Author: Jürgen Jost
Publisher: Springer Science & Business Media
ISBN: 9783642005411
Category: Mathematics
Page: 217
View: 6414
"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.

The Geometry and Physics of Knots

Author: Michael Francis Atiyah
Publisher: Cambridge University Press
ISBN: 9780521395540
Category: Mathematics
Page: 78
View: 9545
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: 1960

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: 6544
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.

Differential Geometry and Mathematical Physics

Part II. Fibre Bundles, Topology and Gauge Fields
Author: Gerd Rudolph,Matthias Schmidt
Publisher: Springer
ISBN: 9402409599
Category: Science
Page: 830
View: 8991
The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

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: 1804
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.

Discrete Integrable Geometry and Physics

Author: Alexander I. Bobenko,Ruedi Seiler
Publisher: Oxford University Press, USA
ISBN: 9780198501602
Category: Mathematics
Page: 370
View: 8324
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 of Physics

An Introduction
Author: Theodore Frankel
Publisher: Cambridge University Press
ISBN: 1139505610
Category: Mathematics
Page: N.A
View: 2157
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

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: 9203
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.

Multivariable Calculus and Mathematica®

With Applications to Geometry and Physics
Author: Kevin R. Coombes,Ronald L. Lipsman,Jonathan M. Rosenberg
Publisher: Springer Science & Business Media
ISBN: 1461216982
Category: Mathematics
Page: 283
View: 438
Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook. The accompanying diskette contains both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students, which can be used with any standard multivariable calculus textbook. It is assumed that students will also have access to an introductory primer for Mathematica.

Algebra, Geometry, and Physics in the 21st Century

Kontsevich Festschrift
Author: Denis Auroux,Ludmil Katzarkov,Tony Pantev,Yan Soibelman,Yuri Tschinkel
Publisher: Birkhäuser
ISBN: 3319599399
Category: Mathematics
Page: 358
View: 9112
This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

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: Arlan Ramsay,Jean Renault
Publisher: American Mathematical Soc.
ISBN: 0821820427
Category: Mathematics
Page: 192
View: 2085
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.

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: 9812772529
Category: Electronic books
Page: 522
View: 4977
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. Sample Chapter(s). Chapter 1: Yangian and Applications (787 KB). Contents: Yangian and Applications (C-M Bai et al.); The Hypoelliptic Laplacian and the ChernOCoGaussOCoBonnet (J-M Bismut); S S Chern and ChernOCoSimos Terms (R Jackiw); Localization and Conjectures from String Duality (K F Liu); Topologization of Electron Liquids with ChernOCoSimons Theory and Quantum Computation (Z H Wang); Topology and Quantum Information (L H Kauffman); Toeplitz Quantization and Symplectic Reduction (X N Ma & W P Zhang); Murphy Operators in Knot Theory (H R Morton); Separation Between Spin and Charge in SU(2) YangOCoMills Theory (A J Niemi); LAwner Equations and Dispersionless Hierarchies (K Takasaki & T Takebe); and other papers. Readership: Graduate students and professional researchers in geometry and physics."

Geometry and Physics

XVI International Fall Workshop
Author: Rui Loja Fernandes,Roger Picken
Publisher: American Inst. of Physics
ISBN: 9780735405462
Category: Science
Page: 228
View: 9092
All papers have been peer-reviewed. The XVI International Fall Workshop on Geometry and Physics brought together geometers and physicists from within and outside the Iberian peninsula, to exchange ideas on how to describe and understand a variety of phenomena in areas such as mechanics or gravity.

Physics, Geometry and Topology

Author: H.C. Lee
Publisher: Springer Science & Business Media
ISBN: 1461538025
Category: Science
Page: 681
View: 745
The Banff NATO Summer School was held August 14-25, 1989 at the Banff Cen tre, Banff, Albert, Canada. It was a combination of two venues: a summer school in the annual series of Summer School in Theoretical Physics spon sored by the Theoretical Physics Division, Canadian Association of Physi cists, and a NATO Advanced Study Institute. The Organizing Committee for the present school was composed of G. Kunstatter (University of Winnipeg), H.C. Lee (Chalk River Laboratories and University of Western Ontario), R. Kobes (University of Winnipeg), D.l. Toms (University of Newcastle Upon Tyne) and Y.S. Wu (University of Utah). Thanks to the group of lecturers (see Contents) and the timeliness of the courses given, the school, entitled PHYSICS, GEOMETRY AND TOPOLOGY, was popular from the very outset. The number of applications outstripped the 90 places of accommodation reserved at the Banff Centre soon after the school was announced. As the eventual total number of participants was increased to 170, it was still necessary to tum away many deserving applicants. In accordance with the spirit of the school, the geometrical and topologi cal properties in each of the wide ranging topics covered by the lectures were emphasized. A recurring theme in a number of the lectures is the Yang-Baxter relation which characterizes a very large class of integrable systems including: many state models, two-dimensional conformal field theory, quantum field theory and quantum gravity in 2 + I dimensions.

Elementary vector analysis

with application to geometry and physics
Author: Charles Ernest Weatherburn
Publisher: N.A
Category: Mathematics
Page: 184
View: 395

Curvature in Mathematics and Physics

Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 0486292711
Category: Mathematics
Page: 416
View: 1470
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Hopf Algebras in Noncommutative Geometry and Physics

Author: Stefaan Caenepeel,Fred Van Oystaeyen
Publisher: CRC Press
ISBN: 9780824757595
Category: Mathematics
Page: 344
View: 2460
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.

Geometry and physics

non-Newtonian forms of dynamics
Author: Asim Orhan Barut
Publisher: Humanities Pr
Category: Mathematics
Page: 123
View: 702

Geometry and Physics of Branes

Author: U Bruzzo,V. Gorini,U. Moschella
Publisher: CRC Press
ISBN: 1420034294
Category: Science
Page: 282
View: 1745
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.