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.


The Geometry of Physics

Filename: the-geometry-of-physics.pdf
ISBN: 0521539277
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.


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.


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.


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.


An Introduction to Spinors and Geometry With Applications in Physics

Filename: an-introduction-to-spinors-and-geometry-with-applications-in-physics.pdf
ISBN: STANFORD:36105030473511
Release Date: 1987
Number of pages: 358
Author: I. Ian M. Benn
Publisher: Institute of Physics Publishing (GB)

Download and read online An Introduction to Spinors and Geometry With Applications in Physics in PDF and EPUB This graduate textbook dealing with the modern mathematical techniques of differential geometry and Clifford algebras is written with students of theoretical physics in mind.


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.


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.


An Introduction to ther Geometry of Numbers

Filename: an-introduction-to-ther-geometry-of-numbers.pdf
ISBN: 3540617884
Release Date: 1996-12-16
Number of pages: 344
Author: J.W.S. Cassels
Publisher: Springer Science & Business Media

Download and read online An Introduction to ther Geometry of Numbers in PDF and EPUB Reihentext + Geometry of Numbers From the reviews: "The work is carefully written. It is well motivated, and interesting to read, even if it is not always easy... historical material is included... the author has written an excellent account of an interesting subject." (Mathematical Gazette) "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowski's Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." (The American Mathematical Monthly)


Gravitational Curvature

Filename: gravitational-curvature.pdf
ISBN: 9780486481210
Release Date: 2011
Number of pages: 172
Author: Theodore Frankel
Publisher: Courier Corporation

Download and read online Gravitational Curvature in PDF and EPUB This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.


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 Symplectic Geometry

Filename: an-introduction-to-symplectic-geometry.pdf
ISBN: 0821820567
Release Date: 2001
Number of pages: 195
Author: Rolf Berndt
Publisher: American Mathematical Soc.

Download and read online An Introduction to Symplectic Geometry in PDF and EPUB Starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kahler manifolds, and coadjoint orbits.Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics.This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations.