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Dirac Operator and Eigenvalues in Riemannian Geometry

Giampiero Esposito
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Abstract

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential operators on manifolds, index of elliptic operators, Dirac operator, index problem for manifolds with a boundary, index of the Dirac operator and anomalies, spectral asymmetry and Riemannian geometry, spectral or local boundary conditions for massless spin-1/2 fields, potentials for massless spin-3/2 fields, conformal anomalies for massless spin-1/2 fields.

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Giampiero Esposito. 1995-07-24. Dirac Operator and Eigenvalues in Riemannian Geometry. https://arxiv.org/abs/gr-qc/9507046

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