Dirac Operators and Index Theory
The physicist P. A. M. Dirac constructed first-order differential operators whose squares were Laplace operators, or more generally wave operators, for the purpose of extending the Schrodinger-Heisenberg quantum mechanics to the relativistic setting. Related operators have been perceived to have central importance in the interface between PDE and differential geometry, and we discuss some of this here.
KeywordsRiemannian Manifold Vector Bundle Line Bundle Dirac Operator Clifford Algebra
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