Lectures on the geometric anatomy of theoretical physics

  • #1
ergospherical
883
1,213
I stumbled across this series of 28 lectures by Dr Frederic Schuller of the university of Twente whilst searching for lectures about Lie theory. Having watched through lectures 13 to 18, I think they are simply superb (of course I'm assuming the rest are of similar quality). I only wish he would also publish the problem sheets he keeps referring to... :oldeyes:

Lecture 01 - Introduction/Logic of Propositions and Predicates
Lecture 02 - Axioms of Set Theory
Lecture 03 - Classification of Sets
Lecture 04 - Topological Spaces - Construction and Purpose
Lecture 05 - Topological Spaces - Some Heavily Used Invariants
Lecture 06 - Topological Manifolds and Manifold Bundles
Lecture 07 - Differential Structures: Definition and Classification
Lecture 08 - Tensor Space Theory I: Over a Field
Lecture 09 - Differential Structures: the Pivotal Concept of Tangent Vector Spaces
Lecture 10 - Construction of the Tangent Bundle
Lecture 11 - Tensor Space Theory II: Over a Ring
Lecture 12 - Grassmann Algebra and deRham Cohomology
Lecture 13 - Lie Groups and Their Lie Algebras
Lecture 14 - Classification of Lie Algebras and Dynkin Diagrams
Lecture 15 - The Lie Group SL(2,C) and its Lie Algebra sl(2,C)
Lecture 16 - Dynkin Diagrams from Lie Algebras, and Vice Versa
Lecture 17 - Representation Theory of Lie Groups and Lie Algebras
Lecture 18 - Reconstruction of a Lie Group from its Algebra
Lecture 19 - Principal Fibre Bundles
Lecture 20 - Associated Fibre Bundles
Lecture 21 - Connections and Connection 1-Forms
Lecture 22 - Local Representations of a Connection on the Base Manifold: Yang-Mills Fields
Lecture 23 - Parallel Transport
Lecture 24 - Curvature and Torsion on Principal Bundles
Lecture 25 - Covariant Derivatives
Lecture 26 - Application: Quantum Mechanics on Curved Spaces
Lecture 27 - Application: Spin Structures
Lecture 28 - Application: Kinematical and Dynamical Symmetries

Here is the playlist:

 
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Answers and Replies

  • #2
14,194
8,184
Thanks for sharing! They look very substantive and interesting.

I’ve watched the first thirty minutes so far and haven't gotten lost and didn't fall asleep so I think that’s a good sign.
 
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