Levinson's theorem as an index pairing
K-Theory and Homology
2023-12-14 v2 Mathematical Physics
math.MP
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 generically have a particular form. As a consequence, Levinson's theorem can be interpreted as the pairing of the -theory class of the unitary scattering operator and the -homology class of the generator of the group of dilations.
Cite
@article{arxiv.2304.04905,
title = {Levinson's theorem as an index pairing},
author = {Angus Alexander and Adam Rennie},
journal= {arXiv preprint arXiv:2304.04905},
year = {2023}
}
Comments
v2: 27 pages, some minor revisions, to appear in J. Funct. Anal