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Dirac Operators with Square-Integrable Potentials

Wednesday 25th July 2012 - 14:00 to 15:00
INI Seminar Room 1
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 $(-\infty,-1]\cup[1,\infty)$. 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.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons