Introduction To Geometrical Physics, An (Second Edition)World Scientific, 2016 M10 7 - 844 pages 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
1 | |
5 | |
DIFFERENTIABLE STRUCTURE | 161 |
NATURES EXTREME GEOMETRIES | 357 |
MATHEMATICAL TOPICS | 379 |
PHYSICAL TOPICS | 555 |
773 | |
791 | |
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Common terms and phrases
abelian basis braid braid group bundle called Chapter commutative compact compact space components configuration space connection consequently consider coordinates corresponding covariant derivative curvature curve defined differentiable manifold dimension dual element equation equivalent euclidean space example exists fiber finite function f gauge theories geodesic geometrical given gravitational group G hamiltonian homeomorphic homotopy identity integral intentionally left blank invariant inverse isomorphic lagrangian Lie algebra Lie derivative Lie group linear loop Lorentz matrix metric Minkowski notation notion obtained open sets operation orthogonal parameter particles phase space physical plane Poincaré polynomials properties quantum quotient representation Section Sitter spacetime special relativity spin structure subgroup subsets subspace Suppose symmetric tangent Teleparallel Gravity tensor theorem topological space topology torsion transformations usual vanishing vector field vector space velocity von Neumann algebras