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Aldrovandi R., Pereira J.G. An Introduction to Geometrical Physics

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Aldrovandi R., Pereira J.G. An Introduction to Geometrical Physics
State University of Sao Paulo, Sao Paulo, Brazil, 1996. – 699 p. – ISBN-10: 9810222327
This work stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and others subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. It consists of a main text and a topical section. The main text introduces the mathematical ideas and serves as a guide to the topical section.
General Topology
Manifolds & Charts
Differentiable Manifolds
Differentiable Structure
Tangent Structure
Differential Forms
Fiber Bundles
Final Touch
Noncommutative Geometry
Mathematical Topics
The Basic Algebraic Structures
Discrete Groups. Braids and Knots
Topological Linear Spaces
Banach Algebras
Variations & Functionals
Functional Forms
Singular Points
Euclidean Spaces and Subspaces
Non-Euclidean Geometries
Physical Topics
Hamiltonian Mechanics
More Mechanics
Statistics and Elasticity
Propagation of Discontinuities
Geometrical Optics
Classical Relativistic Fields
Gauge Fields
General Relativity
De Sitter Spaces
Symmetries on Phase Space
Glossary and Bibliography
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