Topology and Geometry for Physics

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics
Cover of the book Topology and Geometry for Physics by Helmut Eschrig, Springer Berlin Heidelberg
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Author: Helmut Eschrig ISBN: 9783642147005
Publisher: Springer Berlin Heidelberg Publication: January 26, 2011
Imprint: Springer Language: English
Author: Helmut Eschrig
ISBN: 9783642147005
Publisher: Springer Berlin Heidelberg
Publication: January 26, 2011
Imprint: Springer
Language: English

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.

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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.

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