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Geometry and Physics: Cross–Fertilization and Missed Opportunities
Published on Dec 05, 20162652 Views
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Chapter list
Geometry and Physics: Cross-Fertilization and Missed Opportunities00:00
Outline of the Lecture03:32
Bernhard Riemann and the Early Development of Riemannian Geometry04:54
The fundamental document by B. RIEMANN04:56
RICCI’s Absolute Differential Calculus - 108:52
RICCI’s Absolute Differential Calculus - 212:12
RICCI’s Absolute Differential Calculus - 312:19
The Theory of Relativity as Cradle of a New Geometry12:41
The Geometry underlying Special Relativity13:02
The new Geometry behind General Relativity16:12
The Introduction of the Ricci Curvature19:18
The Einstein-Hilbert Equations28:01
What is Special about the Total Scalar Curvature28:35
Cornelius LANCZOS’ Generalized Lagrangians29:04
A Missed Opportunity31:51
The Einstein Equations in the ADM Approach37:05
Asking about the Ricci Flow39:07
On the Way to the Ricci Flow40:55
The Ricci Flow41:00
Attempts of further Generalizations and the Path to Gauge Theories41:37
Hermann WEYL’s attempt for a Further Unification41:40
The Kaluza Ansatz43:28
Bundle Theory48:09
Gauge Theories repeated Appearances in Physics50:01
A striking Result derived from Self-dual Connections51:47
Spinor Fields and Equations involving them55:00
Clifford Algebras and Spinors55:06
Spinors and the Spin Group58:51
W.K. CLIFFORD’s Visionary Note01:00:36
Spinor Fields in Physics01:02:23
Spinor Fields in Mathematics01:05:27
Supersymmetry and Killing Spinors01:07:31
Killing Spinors and Holonomy01:10:03
Concluding Remarks01:12:41
Many other Paths could have been Followed01:12:42
I thank you for your attention01:14:58