Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics

Author: Bernard F. Schutz

Publisher: Cambridge University Press

Published: 1980-01-28

Total Pages: 272

ISBN-13: 1107268141

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In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

Geometrical Methods of Mathematical Physics
Geometrical Methods of Mathematical Physics

Author: Bernard F. Schutz

Publisher: Cambridge University Press

Published: 1980-01-28

Total Pages: 272

ISBN-13: 9780521298872

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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.

Differential Geometry, Differential Equations, and Mathematical Physics
Differential Geometry, Differential Equations, and Mathematical Physics

Author: Maria Ulan

Publisher: Springer Nature

Published: 2021-02-12

Total Pages: 231

ISBN-13: 3030632539

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This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.

Geometry of Classical Fields
Geometry of Classical Fields

Author: Ernst Binz

Publisher: Courier Corporation

Published: 2011-11-30

Total Pages: 474

ISBN-13: 0486150445

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A canonical quantization approach to classical field theory, this text is suitable for mathematicians interested in theoretical physics as well as to theoretical physicists who use differential geometric methods in their modelling. Introduces differential geometry, the theory of Lie groups, and progresses to discuss the systematic development of a covariant Hamiltonian formulation of field theory. 1988 edition.

Differential Geometry and Lie Groups for Physicists
Differential Geometry and Lie Groups for Physicists

Author: Marián Fecko

Publisher: Cambridge University Press

Published: 2006-10-12

Total Pages: 11

ISBN-13: 1139458035

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Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.

Topology and Geometry for Physicists
Topology and Geometry for Physicists

Author: Charles Nash

Publisher: Courier Corporation

Published: 2013-08-16

Total Pages: 302

ISBN-13: 0486318362

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Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.

Differential Geometry, Gauge Theories, and Gravity
Differential Geometry, Gauge Theories, and Gravity

Author: M. Göckeler

Publisher: Cambridge University Press

Published: 1989-07-28

Total Pages: 248

ISBN-13: 9780521378215

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Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Geometric and Topological Methods for Quantum Field Theory
Geometric and Topological Methods for Quantum Field Theory

Author: Sylvie Paycha

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 272

ISBN-13: 0821840622

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This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.