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An introduction to geometrical physics / R. Aldrovandi, J.G. Pereira.

By: Aldrovandi, R. (Ruben)Contributor(s): Pereira, J. GMaterial type: TextTextPublication details: Singapore ; River Edge, N.J. : World Scientific, ©1995. Description: 1 online resource (xvii, 699 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9789812831026; 9812831029Other title: Geometrical physicsSubject(s): Geometry, Differential | Mathematical physics | SCIENCE -- Physics -- Mathematical & Computational | Geometry, Differential | Mathematical physics | Differentialgeometrie | Mathematische Physik | Mathematische fysicaGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Introduction to geometrical physics.DDC classification: 530.1/5636 LOC classification: QC20.7.D52 | A53 1995ebOther classification: 31.81 | SK 370 | SK 950 | SK 990 | UC 100 Online resources: Click here to access online
Contents:
0. Space and geometry -- pt. I. Manifolds. 1. General topology -- 2. Homology -- 3. Homotopy -- 4. Manifolds & charts -- 5. Differentiable manifolds -- pt. II. Differentiable structure. 6. Tangent structure -- 7. Differential forms -- 8. Symmetries -- 9. Fiber bundles -- pt. III. Final touch. 10. Noncommutative geometry -- pt. IV. Mathematical topics. Math. 1. The basic algebraic structures -- Math. 2. Discrete groups. Braids and knots -- Math. 3. Sets and measures -- Math. 4. Topological linear spaces -- Math. 5. Banach algebras -- Math. 6. Representations -- Math. 7. Variations & functionals -- Math. 8. Functional forms -- Math. 9. Singular points -- Math. 10. Euclidean spaces and subspaces -- Math. 11. Non-Euclidean geometries -- Math. 12. Geodesics -- pt. V. Physical topics. Phys. 1. Hamiltonian mechanics -- Phys. 2. More mechanics -- Phys. 3. Statistics and elasticity -- Phys. 4. Propagation of discontinuities -- Phys. 5. Geometrical optics -- Phys. 6. Classical relativistic fields -- Phys. 7. Gauge fields -- Phys. 8. General relativity -- Phys. 9. De Sitter spaces -- Phys. 10. Symmetries on phase space.
Summary: 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.
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Includes bibliographical references (pages 669-682) and index.

Print version record.

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.

0. Space and geometry -- pt. I. Manifolds. 1. General topology -- 2. Homology -- 3. Homotopy -- 4. Manifolds & charts -- 5. Differentiable manifolds -- pt. II. Differentiable structure. 6. Tangent structure -- 7. Differential forms -- 8. Symmetries -- 9. Fiber bundles -- pt. III. Final touch. 10. Noncommutative geometry -- pt. IV. Mathematical topics. Math. 1. The basic algebraic structures -- Math. 2. Discrete groups. Braids and knots -- Math. 3. Sets and measures -- Math. 4. Topological linear spaces -- Math. 5. Banach algebras -- Math. 6. Representations -- Math. 7. Variations & functionals -- Math. 8. Functional forms -- Math. 9. Singular points -- Math. 10. Euclidean spaces and subspaces -- Math. 11. Non-Euclidean geometries -- Math. 12. Geodesics -- pt. V. Physical topics. Phys. 1. Hamiltonian mechanics -- Phys. 2. More mechanics -- Phys. 3. Statistics and elasticity -- Phys. 4. Propagation of discontinuities -- Phys. 5. Geometrical optics -- Phys. 6. Classical relativistic fields -- Phys. 7. Gauge fields -- Phys. 8. General relativity -- Phys. 9. De Sitter spaces -- Phys. 10. Symmetries on phase space.

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