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Geometrical Anatomy of Theoretical Physics

Friedrich–Alexander University Erlangen–Nürnberg via YouTube

Syllabus

Introduction/Logic of propositions and predicates- 01 - Frederic Schuller.
Axioms of set Theory - Lec 02 - Frederic Schuller.
Classification of sets - Lec 03 - Frederic Schuller.
Topological spaces - construction and purpose - Lec 04 - Frederic Schuller.
Topological spaces - some heavily used invariants - Lec 05 - Frederic Schuller.
Topological manifolds and manifold bundles- Lec 06 - Frederic Schuller.
Differentiable structures definition and classification - Lec 07 - Frederic Schuller.
Tensor space theory I: over a field - Lec 08 - Frederic P Schuller.
Differential structures: the pivotal concept of tangent vector spaces - Lec 09 - Frederic Schuller.
Construction of the tangent bundle - Lec 10 - Frederic Schuller.
Tensor space theory II: over a ring - Lec 11 - Frederic Schuller.
Grassmann algebra and deRham cohomology - Lec 12 - Frederic Schuller.
Lie groups and their Lie algebras - Lec 13 - Frederic Schuller.
Classification of Lie algebras and Dynkin diagrams - Lec 14 - Frederic Schuller.
The Lie group SL(2,C) and its Lie algebra sl(2,C) - lec 15 - Frederic Schuller.
Dynkin diagrams from Lie algebras, and vice versa - Lec 16 - Frederic Schuller.
Representation theory of Lie groups and Lie algebras - Lec 17 - Frederic Schuller.
Reconstruction of a Lie group from its algebra - Lec 18 - Frederic Schuller.
Principal fibre bundles - Lec 19 - Frederic Schuller.
Associated fibre bundles - Lec 20 - Frederic Schuller.
Conncections and connection 1-forms - Lec 21 - Frederic Schuller.
Local representations of a connection on the base manifold: Yang-Mills fields - Lec 22.
Parallel transport - Lec 23 - Frederic Schuller.
Curvature and torsion on principal bundles - Lec 24 - Frederic Schuller.
Covariant derivatives - Lec 25 - Frederic Schuller.
Application: Quantum mechanics on curved spaces - Lec 26 - Frederic Schuller.
Application: Spin structures - lec 27 - Frederic Schuller.
Application: Kinematical and dynamical symmetries - Lec 28 - Frederic Schuller.

Taught by

Frederic Schuller

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