Dirac Operators with Square-Integrable Potentials

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• Hughes, D (Cardiff University)
• Wednesday 25 July 2012, 14:00-15:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Spectral Theory of Relativistic Operators

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum $(-infty,-1]p[1,infty)$. The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function. Furthermore, we show that the absolutely continuous spectrum persists when an angular momentum term is added, thus establishing the result for spherically symmetric Dirac operators in higher dimensions, too.

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

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