Year: 2025
Type: article
Abstract: We consider generalised Dirac-Schrödinger operators, consisting of a self-adjoint elliptic first-order differential operator $\mathcal {D}$ with a skew-adjoint ‘potential’ given by a (suitable) family of unbounded operators. The index of such an operator represents the pairing (Kasparov product) of the K-theory class of the potential with the K-homology class of $\mathcal {D}$ . Our main result in this paper is a generalisation of the Callias Theorem: the index of the Dirac-Schrödinger operator can be computed on a suitable compact hypersurface. Our theorem simultaneously generalises (and is inspired by) the well-known result that the spectral flow of a path of relatively compact perturbations depends only on the endpoints.
Source: Forum of Mathematics Sigma
Author: Koen van den Dungen
Institution: University of Bonn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,650
OpenAlex ID: W4406810162