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Differencial Geometry and Fields

Code 13320
Year 1
Semester S1
ECTS Credits 10
Workload OT(30H)/TP(30H)
Scientific area Física e Matemática
Entry requirements None
Learning outcomes To address the fundamentals of differential geometry.
To address the mathematical foundations of theories of connections
and associated techniques.
To address General Relativity from a mathematical-physics perspective.
Syllabus 1. Manifolds
2. Fiber bundles
3. Tensors and forms
4. Connections
5. Semi-riemannian manifolds
6. General Relativity
Main Bibliography T Eguchi, PB Gilkey, AJ Hanson 1980 Gravitation, Gauge Theories and Differential Geometry
(Physics Reports 66, No. 6, 213-393)
B Felsager 1998 Geometry, Particles, and Fields, Springer
M Göckeler, T Schücker 1989 Differential Geometry, Gauge Theories, and Gravity, Cambridge
CJ Isham 1999 Modern Differential Geometry for Physicists 2ed, World Scientific
S Kobayashi, K Nomizu 1996 Foundations of Differential Geometry I & II, Wiley
LD Landau, EM Lifshitz 1980 The Classical Theory of Fields 4ed, Butterworth-Heinemann
CW Misner, KS Thorne, JA Wheeler 1973 Gravitation, WH Freeman and Company
B O’Neill 1983 Semi-Riemannian Geometry with Applications to Relativity, Academic Press
G Rudolph, M Schmidt 2013 Differential Geometry and Mathematical Physics I & II, Springer
BF Schutz 1980 Geometrical Methods of Mathematical Physics, Cambridge Univ.Press
P Szekeres 2012 A Course in Modern Mathematical Physics, Cambridge Univ.Press
RM Wald 1984 General Relativity, The Univ. of Chicago Press
Teaching Methodologies and Assessment Criteria The classes will be tutorials. The contents of the program will be studied autonomously by the student following the bibliography suggested by the teacher. In order to monitor and evaluate the student's understanding, will be propose lists of exercises that the student will solve. In the classes the teacher will present additional topics that complement and deepen the study done by the student and the doubts present will be discussed and clarified. The evaluation will consist of two moments: Exercise lists (L) and presentation of a seminar (S). The final classification will be CF=(0.5*L+0.5*S). The student may also take a final exam.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2019-07-04

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