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Session S30 - Mathematical Methods in Quantum Mechanics

Monday, July 19, 17:30 ~ 18:10 UTC-3

Continuity properties of the spectral shift function for massless Dirac operators and an application to the Witten index

Fritz Gesztesy

Baylor University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We report on recent results regarding the limiting absorption principle for multi-dimensional, massless Dirac-type operators (implying absence of singularly continuous spectrum) and continuity properties of the associated spectral shift function.

We will motivate our interest in this circle of ideas by briefly describing the connection to index theory for non-Fredholm operators, particularly, to the notion of the Witten index.

This is based on various joint work with A. Carey, J. Kaad, G. Levitina, R. Nichols, D. Potapov, F. Sukochev, and D. Zanin.

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