【理论物理的几何剖析】【FAU】Geometric Anatomy of Theoretical Physics by Fredric Schuller
https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic
This course was given by Fredric Schuller at Friedrich-Alexander-Universität Erlangen-Nürnberg.
视频选集
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Introduction-Logic of propositions and predicates
01:40:48
Axioms of set Theory
01:51:56
Classification of sets
01:34:41
Topological spaces_construction and purpose
01:38:42
Topological spaces_some heavily used invariants
01:56:43
Topological manifolds and manifold bundles
01:49:18
Differentiable structures definition and classification
01:14:34
Tensor space theory I_over a field
02:22:59
Differential structures_the pivotal concept of tangent vector spaces
01:44:14
Construction of the tangent bundle
01:48:50
Tensor space theory II_over a ring
01:55:10
Grassmann algebra and deRham cohomology
01:47:19
Lie groups and their Lie algebras
01:43:12
Classification of Lie algebras and Dynkin diagrams
01:46:43
The Lie group SL(2,C) and its Lie algebra sl(2,C)
01:51:13
Dynkin diagrams from Lie algebras, and vice versa
01:40:32
Representation theory of Lie groups and Lie algebras
01:32:38
Reconstruction of a Lie group from its algebra
44:10
Principal fibre bundles
02:33:32
Associated fibre bundles
01:42:31
Conncections and connection 1-forms
01:05:00
Local representations of a connection on the base manifold_Yang-Mills fields
01:29:33
Parallel transport
01:44:31
Curvature and torsion on principal bundles
01:16:09
Covariant derivatives
01:16:36
Application: Quantum mechanics on curved spaces
01:32:15
Application: Spin structures
01:39:15
Application: Kinematical and dynamical symmetries
01:32:47
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