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arXiv · 2304.04905

Levinson's theorem as an index pairing

Angus Alexander·Adam Rennie
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Abstract

We build on work of Kellendonk, Richard, Tiedra de Aldecoa and others to show that the wave operators for Schr\"{o}dinger scattering theory on $\mathbb{R}^n$ generically have a particular form. As a consequence, Levinson's theorem can be interpreted as the pairing of the $K$-theory class of the unitary scattering operator and the $K$-homology class of the generator of the group of dilations.

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Angus Alexander, Adam Rennie. 2023-04-11. Levinson's theorem as an index pairing. https://doi.org/10.1016/j.jfa.2023.110287

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