Dirac Operator and Eigenvalues in Riemannian Geometry

Details Dirac Operator and Eigenvalues in Riemannian Geometry Dirac Operator and Eigenvalues in Riemannian Geometry

1995-07-24

arxiv.org/abs/gr-qc/9507046v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

105 pages, plain-tex, based on 5 graduate lectures given by the author at SISSA, Trieste, April 1994

Scientific paper

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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