Dirac Operators and Index Theory

  • Michael E. Taylor
Part of the Applied Mathematical Sciences book series (AMS, volume 116)


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.


Riemannian Manifold Vector Bundle Line Bundle Dirac Operator Spin Structure 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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