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Geometric Anatomy of Theoretical Physics (2015, University of Erlangen-Nurnberg). Instructor: Dr. Frederic Schuller.
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Description
Theoretical physics aims to provide proper mathematical language for classical mechanics, electromagnetism, quantum mechanics, and statistical physics. This course focuses on the development of differential geometry discussing topics on logic, set theory, topology, topological manifolds, differentiable manifolds, bundles, and geometry.
Course content
- Lecture 01 – Introduction/Logic of Propositions and Predicates Unlimited
- Lecture 02 – Axioms of Set Theory Unlimited
- Lecture 03 – Classification of Sets Unlimited
- Lecture 04 – Topological Spaces – Construction and Purpose Unlimited
- Lecture 05 – Topological Spaces – Some Heavily Used Invariants Unlimited
- Lecture 06 – Topological Manifolds and Manifold Bundles Unlimited
- Lecture 07 – Differential Structures: Definition and Classification Unlimited
- Lecture 08 – Tensor Space Theory I: Over a Field Unlimited
- Lecture 09 – Differential Structures: the Pivotal Concept of Tangent Vector Spaces Unlimited
- Lecture 10 – Construction of the Tangent Bundle Unlimited
- Lecture 11 – Tensor Space Theory II: Over a Ring Unlimited
- Lecture 12 – Grassmann Algebra and deRham Cohomology Unlimited
- Lecture 13 – Lie Groups and Their Lie Algebras Unlimited
- Lecture 14 – Classification of Lie Algebras and Dynkin Diagrams Unlimited
- Lecture 15 – The Lie Group SL(2,C) and its Lie Algebra SL(2,C) Unlimited
- Lecture 16 – Dynkin Diagrams from Lie Algebras, and Vice Versa Unlimited
- Lecture 17 – Representation Theory of Lie Groups and Lie Algebras Unlimited
- Lecture 18 – Reconstruction of a Lie Group from its Algebra Unlimited
- Lecture 19 – Principal Fibre Bundles Unlimited
- Lecture 20 – Associated Fibre Bundles Unlimited
- Lecture 21 – Connections and Connection 1-Forms Unlimited
- Lecture 22 – Local Representations of a Connection on the Base Manifold: Yang-Mills Fields Unlimited
- Lecture 23 – Parallel Transport Unlimited
- Lecture 24 – Curvature and Torsion on Principal Bundles Unlimited
- Lecture 25 – Covariant Derivatives Unlimited
- Lecture 26 – Application: Quantum Mechanics on Curved Spaces Unlimited
- Lecture 27 – Application: Spin Structures Unlimited
- Lecture 28 – Application: Kinematical and Dynamical Symmetries Unlimited
Instructor
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