Lectures on Geometrical Anatomy of Theoretical Physics

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Curated by: Frederic Schuller (28 videos)

Currently Playing: Grassmann algebra and deRham cohomology - Lec 12 - Frederic Schuller

This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller

Tracks in this Playlist

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