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Mathematical Physics : Lectures in Physics - Robert Geroch

Mathematical Physics

Lectures in Physics

Paperback Published: 1st January 1984
ISBN: 9780226288628
Number Of Pages: 358

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Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.

Introduction
Categories
The Category of Groups
Subgroups
Normal Subgroups
Homomorphisms
Direct Products and Sums of Groups
Relations
The Category of Vector Spaces
Subspaces
Linear Mappings; Direct Products and Sums
From Real to Complex Vector Spaces and Back
Duals
Multilinear Mappings; Tensor Products
Example: Minkowski Vector Space
Example: The Lorentz Group
Functors
The Category of Associative Algebras
The Category of Lie Algebras
Example: The Algebra of Observables
Example: Fock Vector Space
Representations: General Theory
Representations on Vector Spaces
The Algebraic Categories: Summary
Subsets and Mappings
Topological Spaces
Continuous Mappings
The Category of Topological Spaces
Nets
Compactness
The Compact-Open Topology
Connectedness
Example: Dynamical Systems
Homotopy
Homology
Homology: Relation to Homotopy
The Homology Functors
Uniform Spaces
The Completion of a Uniform Space
Topological Groups
Topological Vector Spaces
Categories: Summary
Measure Spaces
Constructing Measure Spaces
Measurable Functions
Integrals
Distributions
Hilbert Spaces
Bounded Operators
The Spectrum of a Bounded Operator
The Spectral Theorem: Finite-dimensional Case
Continuous Functions of a Hermitian Operator
Other Functions of a Hermitian Operator
The Spectral Theorem
Operators (Not Necessarily Bounded)
Self-Adjoint Operators
Index of Defined Terms
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780226288628
ISBN-10: 0226288625
Series: Lectures in Physics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 358
Published: 1st January 1984
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 23.1 x 15.5  x 1.91
Weight (kg): 0.47

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