Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 The concept of a manifold
- 2 Vector and tensor fields
- 3 Mappings of tensors induced by mappings of manifolds
- 4 Lie derivative
- 5 Exterior algebra
- 6 Differential calculus of forms
- 7 Integral calculus of forms
- 8 Particular cases and applications of Stokes' theorem
- 9 Poincaré lemma and cohomologies
- 10 Lie groups: basic facts
- 11 Differential geometry on Lie groups
- 12 Representations of Lie groups and Lie algebras
- 13 Actions of Lie groups and Lie algebras on manifolds
- 14 Hamiltonian mechanics and symplectic manifolds
- 15 Parallel transport and linear connection on M
- 16 Field theory and the language of forms
- 17 Differential geometry on TM and T *M
- 18 Hamiltonian and Lagrangian equations
- 19 Linear connection and the frame bundle
- 20 Connection on a principal G-bundle
- 21 Gauge theories and connections
- 22 Spinor fields and the Dirac operator
- Appendix A Some relevant algebraic structures
- Appendix B Starring
- Bibliography
- Index of (frequently used) symbols
- Index
Appendix B - Starring
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- Introduction
- 1 The concept of a manifold
- 2 Vector and tensor fields
- 3 Mappings of tensors induced by mappings of manifolds
- 4 Lie derivative
- 5 Exterior algebra
- 6 Differential calculus of forms
- 7 Integral calculus of forms
- 8 Particular cases and applications of Stokes' theorem
- 9 Poincaré lemma and cohomologies
- 10 Lie groups: basic facts
- 11 Differential geometry on Lie groups
- 12 Representations of Lie groups and Lie algebras
- 13 Actions of Lie groups and Lie algebras on manifolds
- 14 Hamiltonian mechanics and symplectic manifolds
- 15 Parallel transport and linear connection on M
- 16 Field theory and the language of forms
- 17 Differential geometry on TM and T *M
- 18 Hamiltonian and Lagrangian equations
- 19 Linear connection and the frame bundle
- 20 Connection on a principal G-bundle
- 21 Gauge theories and connections
- 22 Spinor fields and the Dirac operator
- Appendix A Some relevant algebraic structures
- Appendix B Starring
- Bibliography
- Index of (frequently used) symbols
- Index
Summary
Abel, Niels Hendrik, 1802 Finnøy–1829 Froland
Ampère, Marie Andrè, 1775 Lyon–1836 Marseilles
Atiyah, Michael Francis, 1929 London
Beltrami, Eugenio, 1835 Cremona–1900 Rome
Betti, Enrico, 1823 Pistoia–1892 Soiana
Bianchi, Luigi, 1856 Parma–1928 Pisa
Carathéodory, Constantin, 1873 Berlin–1950 Munich
Cartan, Elie Joseph, 1869 Dolomieu–1951 Paris
Cauchy, Augustin Louis, 1789 Paris–1857 Sceaux (Paris)
Christoffel, Elwin Bruno, 1829 Montjoie Aachen–1900 Strasbourg
Clebsch, Rudolf Friedrich Alfred, 1833 Königsberg–1872 Göttingen
Clifford, William Kingdon, 1845 Exeter–1879 Madeira
Coriolis, Gaspard Gustave de, 1792 Paris–1843 Paris
Coulomb, Charles Augustin de, 1736 Angoulême–1806 Paris
d'Alembert, Jean Le Rond, 1717 Paris–1783 Paris
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Descartes, René, 1596 La Haye–1650 Stockholm
Dirac, Paul Adrien Maurice, 1902 Bristol–1984 Tallahassee
Einstein, Albert, 1879 Ulm–1955 Princeton
Euclid, circa 325 BC (?)–circa 265 BC (?) Alexandria
Euler, Leonhard, 1707 Basel–1783 St Petersburg
Faraday, Michael, 1791 Newington Butts–1867 Hampton Court
Foucault, Jean Bernard Léon, 1819 Paris–1868 Paris
Fourier, Jean Baptiste Joseph, 1768 Auxerre–1830 Paris
Frobenius, Ferdinand Georg, 1849 Berlin–Charlottenburg–1917 Berlin
Gauss, Johann Carl Friedrich, 1777 Brunswick–1855 Göttingen
Gordan, Paul Albert, 1837 Breslau–1912 Erlangen
Gordon, Walter, 1893 Apolda–1939 Stockholm
Grassmann, Herman Günter, 1809 Stettin–1877 Stettin
Green, George, 1793 Sneinton–1841 Sneinton
Hamilton, William Rowan, 1805 Dublin–1865 Dublin
Hausdorff, Felix, 1868 Breslau–1942 Bonn
Heaviside, Oliver, 1850 Camden Town (London)–1925 Torquay
Heisenberg, Werner Karl, 1901 Wörzburg–1976 Münich
Helmholtz, Hermann Ludwig Ferdinand von, 1821 Potsdam–1894 Berlin
Hilbert, David, 1862 Königsberg–1943 Göttingen
Hodge, William Vallance Douglas, 1903 Edinburgh–1975 Cambridge
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- Information
- Differential Geometry and Lie Groups for Physicists , pp. 683 - 684Publisher: Cambridge University PressPrint publication year: 2006