An Introduction To Geometrical PhysicsWorld Scientific, 1995 M10 31 - 720 pages This book 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 other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students. |
Contents
| 1 | |
| 5 | |
PART II DIFFERENTIABLE STRUCTURE | 143 |
PART III FINAL TOUCH | 339 |
PART IV MATHEMATICAL TOPICS | 349 |
PART V PHYSICAL TOPICS | 507 |
GLOSSARY | 661 |
| 669 | |
| 683 | |
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Common terms and phrases
abelian antisymmetric braid group bundle called canonical cartesian commutative compact compact space components configuration space connection consequently consider coordinates corresponding covariant derivative curvature curve defined definition deformation differentiable manifold dimension dimensional dual element equation equivalent euclidean space example exists fiber Figure finite function f fundamental group geodesic geometrical given group G hamiltonian Hilbert space homeomorphic homotopy identity integral invariant inverse isomorphic lagrangian lattice Lie algebra Lie derivative Lie group loop mapping f matrix metric natural basis neighbourhood notation obtained open sets operation orthogonal p-form particles path phase space physical plane Poincaré Poisson bracket polynomials principal bundle properties quantum quotient representation simple spacetime sphere structure subgroup subsets subspace Suppose symmetric symplectic tangent tensor theorem topological space topology torsion transformations trivial usual vanishing vector field vector space velocity vertices von Neumann algebras wavefunction zero