Lectures on Geometrical Anatomy of Theoretical Physics

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Curated by: Frederic Schuller (28 videos)

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• 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