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

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Aldrovandi R., Pereira J. An Introduction to Geometrical Physics
Second Edition. — World Scientific Publishing, 2017. — 813 p. — ISBN 978-981-3146-80-8
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 — gravitational, electromagnetic, strong nuclear, and weak nuclear.
The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students.
In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Contents:
Manifolds:
General Topology
Homology
Homotopy
Manifolds and Charts
Differentiable Manifolds
Differentiable Structure:
Tangent Structure
Differential Forms
Symmetries
Fiber Bundles
Nature's Extreme Geometries:
Quantum Geometry
Cosmology: the Standard Model
Planck Scale Kinematics
Mathematical Topics:
The Basic Algebraic Structures
Discrete Groups: Braids and Knots
Sets and Measures
Topological Linear Spaces
Banach Algebras
Representations
Variations and Functionals
Functional Forms
Singular Points
Euclidian Spaces and Subspaces
Non-Euclidian Geometries
Geodesics
Physical Topics:
Hamiltonian Mechanics
More Mechanics
Symmetries in Phase Space
Statistics and Elasticity
Propagation of Discontinuities
Geometrical Optics
Classical Relativistic Fields
Gauge Fields: Fundamentals
More Gauge Fields: Wu-Yang Copies
General Relativity
Teleparallel Gravity
Einstein–Cartan Theory
de Sitter Invariant Special Relativity
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