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From Crystal Optics to Dirac Operators--A Spectral Theory

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Spectral Theory of Relativistic Operators

A unified approach to first-order systems of classical physics is presented. Dirac operators are included, but there is no need for the fact that the square is the Laplacian (+ constant). The main tool is a derivation of the Limiting Absorption Principle, using the geometry of the characteristic surfaces and the trace lemma. As an application, global spacetime estimates are derived, in weighted Sobolev spaces.

This talk is part of the Isaac Newton Institute Seminar Series series.

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