The Geometry of Physics

Filename: the-geometry-of-physics.pdf
ISBN: 9781139505611
Release Date: 2011-11-03
Number of pages:
Author: Theodore Frankel
Publisher: Cambridge University Press

Download and read online The Geometry of Physics in PDF and EPUB 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.


The Geometry of Physics

Filename: the-geometry-of-physics.pdf
ISBN: 9780521539272
Release Date: 2004
Number of pages: 694
Author: Theodore Frankel
Publisher: Cambridge University Press

Download and read online The Geometry of Physics in PDF and EPUB 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 deformation tensors of elasticity, soap films, special and general relativity, 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; consequently, the book should be of interest also to mathematics students. Ideal for graduate and advanced undergraduate students of physics, engineering and mathematics as a course text or for self study.


Geometry and Physics

Filename: geometry-and-physics.pdf
ISBN: 3642005411
Release Date: 2009-08-17
Number of pages: 217
Author: Jürgen Jost
Publisher: Springer Science & Business Media

Download and read online Geometry and Physics in PDF and EPUB "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 of Spacetime

Filename: the-geometry-of-spacetime.pdf
ISBN: 9781475767360
Release Date: 2013-03-09
Number of pages: 463
Author: James J. Callahan
Publisher: Springer Science & Business Media

Download and read online The Geometry of Spacetime in PDF and EPUB Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.


Lie Groups Physics and Geometry

Filename: lie-groups-physics-and-geometry.pdf
ISBN: 9781139469074
Release Date: 2008-01-17
Number of pages:
Author: Robert Gilmore
Publisher: Cambridge University Press

Download and read online Lie Groups Physics and Geometry in PDF and EPUB Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.


The Geometry and Physics of Knots

Filename: the-geometry-and-physics-of-knots.pdf
ISBN: 0521395542
Release Date: 1990-08-23
Number of pages: 78
Author: Michael Francis Atiyah
Publisher: Cambridge University Press

Download and read online The Geometry and Physics of Knots in PDF and EPUB 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.


Topology and Geometry for Physics

Filename: topology-and-geometry-for-physics.pdf
ISBN: 9783642146992
Release Date: 2011-02-09
Number of pages: 389
Author: Helmut Eschrig
Publisher: Springer Science & Business Media

Download and read online Topology and Geometry for Physics in PDF and EPUB A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.


Geometrical Methods of Mathematical Physics

Filename: geometrical-methods-of-mathematical-physics.pdf
ISBN: 0521298873
Release Date: 1980-01-28
Number of pages: 250
Author: Bernard F. Schutz
Publisher: Cambridge University Press

Download and read online Geometrical Methods of Mathematical Physics in PDF and EPUB For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.


Geometry of Quantum States

Filename: geometry-of-quantum-states.pdf
ISBN: 9781139453462
Release Date: 2007-12-06
Number of pages:
Author: Ingemar Bengtsson
Publisher: Cambridge University Press

Download and read online Geometry of Quantum States in PDF and EPUB Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.


An Introduction to the Geometry of Numbers

Filename: an-introduction-to-the-geometry-of-numbers.pdf
ISBN: 9783642620355
Release Date: 2012-12-06
Number of pages: 345
Author: J.W.S. Cassels
Publisher: Springer Science & Business Media

Download and read online An Introduction to the Geometry of Numbers in PDF and EPUB From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly


Topology and Geometry for Physicists

Filename: topology-and-geometry-for-physicists.pdf
ISBN: 9780486318363
Release Date: 2013-08-16
Number of pages: 320
Author: Charles Nash
Publisher: Courier Corporation

Download and read online Topology and Geometry for Physicists in PDF and EPUB Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.


The Geometry of Minkowski Spacetime

Filename: the-geometry-of-minkowski-spacetime.pdf
ISBN: 0486432351
Release Date: 2003
Number of pages: 257
Author: Gregory L. Naber
Publisher: Courier Corporation

Download and read online The Geometry of Minkowski Spacetime in PDF and EPUB This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.


An Introduction to Geometrical Physics

Filename: an-introduction-to-geometrical-physics.pdf
ISBN: 9789813146839
Release Date: 2016-10-07
Number of pages: 844
Author: Ruben Aldrovandi
Publisher: World Scientific

Download and read online An Introduction to Geometrical Physics in PDF and EPUB ' This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature — gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding. Contents:Manifolds:General TopologyHomologyHomotopyManifolds and ChartsDifferentiable ManifoldsDifferentiable Structure:Tangent StructureDifferential FormsSymmetriesFiber BundlesNature''s Extreme Geometries:Quantum GeometryCosmology: the Standard ModelPlanck Scale KinematicsMathematical Topics:The Basic Algebraic StructuresDiscrete Groups: Braids and KnotsSets and MeasuresTopological Linear SpacesBanach AlgebrasRepresentationsVariations and FunctionalsFunctional FormsSingular PointsEuclidian Spaces and SubspacesNon-Euclidian GeometriesGeodesicsPhysical Topics:Hamiltonian MechanicsMore MechanicsSymmetries in Phase SpaceStatistics and ElasticityPropagation of DiscontinuitiesGeometrical OpticsClassical Relativistic FieldsGauge Fields: FundamentalsMore Gauge Fields: Wu-Yang CopiesGeneral RelativityTeleparallel GravityEinstein–Cartan Theoryde Sitter Invariant Special Relativity Readership: Graduate students and researchers. '


An Introduction to Differential Geometry and Topology in Mathematical Physics

Filename: an-introduction-to-differential-geometry-and-topology-in-mathematical-physics.pdf
ISBN: 9789814495806
Release Date: 1999-01-18
Number of pages: 220
Author: Wang Rong
Publisher: World Scientific

Download and read online An Introduction to Differential Geometry and Topology in Mathematical Physics in PDF and EPUB This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics. Contents:Differential Manifolds:Preliminary Knowledge and DefinitionsProperties and Operations of Tangent Vectors and Cotangent VectorsCurvature Tensors, Torsion Tensors, Covariant Differentials and Adjoint Exterior DifferentialsRiemannian GeometryComplex ManifoldGlobal Topological Properties:Homotopy Equivalence and Homotopy Groups of ManifoldsHomology and de Rham CohomologyFibre Bundles and Their Topological StructuresConnections and Curvatures on Fibre BundlesCharacteristic Classes of Fibre BundlesIndex Theorem and 4-Manifolds:Index Theorems for Manifolds Without BoundaryEssential Features of 4-Manifolds Readership: Mathematicians and physicists. Keywords:Homotopy Theory;Index Theorems;Riemannian Geometry;Complex Manifolds;Homology;De Rham Cohomology;Fibre Bundles;Characteristic Classes


Applied Differential Geometry

Filename: applied-differential-geometry.pdf
ISBN: 0521269296
Release Date: 1985-05-31
Number of pages: 414
Author: William L. Burke
Publisher: Cambridge University Press

Download and read online Applied Differential Geometry in PDF and EPUB This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.