Summary: 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.
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 Read Now ». Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. 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.
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 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.
This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry. Bibliography and Notes An excellent elementary introduction to the concepts of this chapter from a physics point of view is Bernard F.
Author : Theodore Frankel Publisher: Cambridge University Press ISBN: Category: Mathematics Page: View: Read Now » 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. Vernon Spickard. Things I want to See. Where Should I Go Next? Up to the Minute! Use this gadget to give up to the minute changes in your plans, inspirational thoughts or simply a quick update of your latest adventure.
Ways to Reach Me. Recent site activity View All. First variation Hb : X First version Pb : Show description. Minimal surfaces and Teichmuller theory. The notes from a suite of lectures writer added at nationwide Tsing-Hua collage in Hsinchu, Taiwan, within the spring of Complex, contact and symmetric manifolds: In honor of L. This e-book is concentrated at the interrelations among the curvature and the geometry of Riemannian manifolds. It comprises examine and survey articles in keeping with the most talks added on the foreign Congress.
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