| Center |
| Faculty of Physics |
| Departament |
| Theoretical Physics |
| Lecturers in charge |
| E4020 - JOSE ADOLFO AZCARRAGA FELIU |
| Met. Docent |
| There will be a single examination, at the end of course, that will include theoretical questions and more practical ones. The final qualification will also consider the personal homework. |
| Met. Avaluació |
| - - |
| Bibliografia |
| Y. Choquet-Bruhat, C. De Witt-Morette y M. Dillard-Bleick: Analysis, Manifolds and Physics, North Holland (1977) R. Abraham y J. Marsden: Foundations of Mechanics, Benjamin-Cummings, London (1978) (caps. 1 y 2) B.A. Dubrovin, A.T. Fomenko, S.P. Novikov: Modern Geometry -Methods and applications I, Springer Verlag (1992) J.A. de Azcárraga y J. M. Izquierdo: Lie groups, Lie algebras, cohomology and some applications in physics, Cambridge monographs in math. phys., Camb. Univ. Press (segunda ed., 1998, cap. 1) L.S. Pontriaguin: Grupos continuos, Mir, Moscú (1978) (existe edición inglesa, con correcciones: Topological groups, Gordon and Breach (1966)). H. Weyl: The theory of Groups and Quantum Mechanics, Dover, N.Y. (1931/50). H. Bacry: loc. cit. (A |
| Continguts |
| 1. Differential forms and Cartan calculus. 2 Groups and Lie algebras. 3 Representation Theory. 4 Simple Lie Algebras and their classification 5 Finite irreducible Representations of simple Lie algebras. 6 Example: study of the SU(3)algebra. 7 The Lorentz group and the SL(2, c) group 8 Galileo and Poincaré Groups. Representations. Conformal Group. 9 Introduction to the supermanifolds and graduate groups 10 Fibre bundles. 11 Connections on a fibre bundle. 12 Physical Applications |