Spectral flow for skew-adjoint Fredholm operators

  • Alan L. Carey

    Australian National University, Canberra, Australia and University of Wollongong, Australia
  • John Phillips

    University of Victoria, Canada
  • Hermann Schulz-Baldes

    Universität Erlangen-Nürnberg, Germany
Spectral flow for skew-adjoint Fredholm operators cover

A subscription is required to access this article.

Abstract

An analytic definition of a -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 -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 -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 -polarization in these models.

Cite this article

Alan L. Carey, John Phillips, Hermann Schulz-Baldes, Spectral flow for skew-adjoint Fredholm operators. J. Spectr. Theory 9 (2019), no. 1, pp. 137–170

DOI 10.4171/JST/243