# InfoCoBuild

## Geometric Anatomy of Theoretical Physics

Geometric Anatomy of Theoretical Physics (2015, University of Erlangen-Nurnberg). Instructor: Dr. Frederic Schuller. 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.

 Introduction

 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