Spectral flow for skew-adjoint Fredholm operators

Authors

Alan L. Carey, Australian National University, University of WollongongFollow
John Phillips, University of Victoria, Canada
Hermann Schulz-Baldes, Friedrich-Alexander-University of Erlangen-Nuremberg

RIS ID

132851

Publication Details

Carey, A. L., Phillips, J. & Schulz-Baldes, H. (2019). Spectral flow for skew-adjoint Fredholm operators. Journal of Spectral Theory, 9 (1), 137-170.

Abstract

An analytic definition of a Z₂-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through 0 along the path. The Z₂-valued spectral flow is shown to satisfy a concatenation property and homotopy invariance, and it provides an isomorphism on the fundamental group of the real skew-adjoint Fredholm operators. Moreover, it is connected to a Z₂-index pairing for suitable paths. Applications concern the zero energy bound states at defects in a Majorana chain and a spectral flow interpretation for the Z₂-polarization in these models.