Spinors in Physics and Geometry
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Description: A fourth year math/physics course at UIUC with online lecture notes.
Spin Geometry in Math and Physics Spinors in Geometry and Physics Spinors have played a crucial role in both the physics and the mathematics of the 20th century. Discovered in 1913 by Cartan in his investigations of the representation theory of the orthogonal groups, spinors first appeared in physics in the 1920's in the guise of Pauli's spin matrices and in Dirac's relativistic theory of electron spin. Since that time, spinors, spin structures and their attendant Dirac operators have remained of fundamental importance in quantum physics and in many areas of mathematics, especially those dealing with the relation between geometry, topology and analysis. In mathematics they provide key insights into many questions, including index theorems for elliptic operators, the integrality of characteristic numbers, existence of metrics of positive scalar curvature, twistor spaces, and (most recently) Seiberg-Witten theory.
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| Page title: | Spin Geometry in Math and Physics |
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| Date | activated: 18-Jul-1985 last updated: 22-Mar-2011 expires: 31-Jul-2014 |