Lectures on the geometric anatomy of theoretical physics

In summary, the conversation was about a series of 28 lectures by Dr. Frederic Schuller from the University of Twente on Lie theory. The person who stumbled upon the lectures found lectures 13-18 to be superb and wished Dr. Schuller would publish the problem sheets he referred to. The lectures cover various topics such as topology, differential structures, tensor space theory, Lie groups and algebras, and applications in quantum mechanics and spin structures. The person also shared links to Dr. Schuller's profile and a Facebook fan page dedicated to him.
  • #1
ergospherical
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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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  • #2
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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1. What is the purpose of "Lectures on the geometric anatomy of theoretical physics"?

The purpose of these lectures is to provide a comprehensive understanding of the geometric principles and concepts that underlie theoretical physics. It aims to bridge the gap between abstract mathematical concepts and their application in the physical world.

2. Who are the intended audience for these lectures?

The intended audience for these lectures are students and researchers in the field of theoretical physics who have a basic understanding of mathematical concepts and are looking to deepen their knowledge of the geometric foundations of the subject.

3. What topics are covered in "Lectures on the geometric anatomy of theoretical physics"?

These lectures cover a wide range of topics including differential geometry, topology, group theory, and symplectic geometry. It also explores the application of these concepts in various areas of theoretical physics such as quantum mechanics, general relativity, and gauge theories.

4. Are there any prerequisites for understanding these lectures?

A basic understanding of mathematics, specifically calculus and linear algebra, is necessary to fully comprehend the material presented in these lectures. Familiarity with concepts in physics, such as classical mechanics and electromagnetism, would also be beneficial.

5. How can these lectures be useful for researchers in the field of theoretical physics?

These lectures provide a comprehensive and in-depth understanding of the geometric foundations of theoretical physics, which can aid researchers in developing new theories and models. It also offers a new perspective on familiar concepts, potentially leading to new insights and discoveries.

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