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source: Fredric Schuller 2015年9月21日
"Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr. Frederic P Schuller
Introduction/Logic of propositions and predicates- 01 1:40:48
Axioms of set Theory - Lec 02 1:51:56
Classification of sets - Lec 03 1:34:42
Topological spaces - construction and purpose - Lec 04 1:38:42
Topological spaces - some heavily used invariants - Lec 05 1:56:44
Topological manifolds and manifold bundles- Lec 06 1:49:18
Differentiable structures definition and classification - Lec 07 1:14:34
Tensor space theory I: over a field - Lec 08 2:22:59
Differential structures: the pivotal concept of tangent vector spaces - Lec 09 1:44:15
Construction of the tangent bundle - Lec 10 1:48:50
Tensor space theory II: over a ring - Lec 11 1:55:10
Grassmann algebra and deRham cohomology - Lec 12 1:47:19
Lie groups and their Lie algebras - Lec 13 1:43:12
Classification of Lie algebras and Dynkin diagrams - Lec 14 1:46:43
The Lie group SL(2,C) and its Lie algebra sl(2,C) - lec 15 1:51:13
Dynkin diagrams from Lie algebras, and vice versa - Lec 16 1:40:32
Representation theory of Lie groups and Lie algebras - Lec 17 1:32:39
Reconstruction of a Lie group from its algebra - Lec 18 44:10
Principal fibre bundles - Lec 19 2:33:32
Associated fibre bundles - Lec 20 1:42:31
Conncections and connection 1-forms - Lec 21 1:05:01
Local representations of a connection on the base manifold: Yang-Mills fields - Lec 22 1:29:33
Parallel transport - Lec 23 1:44:32
Curvature and torsion on principal bundles - Lec 24 1:16:10
Covariant derivatives - Lec 25 1:16:36
Application: Quantum mechanics on curved spaces - Lec 26 1:32:16
Application: Spin structures - lec 27 1:39:15
Application: Kinematical and dynamical symmetries - Lec 28 - Frederic Schuller 1:32:48
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