Spectral flow for skew-adjoint Fredholm operators

Carey AL, Phillips J, Schulz-Baldes H (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Spectral Theory European Mathematical Society

Book Volume: 9

Pages Range: 137-170

Journal Issue: 1

DOI: 10.4171/JST/243

Abstract

An analytic definition of a Z 2 -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 Z 2 -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 Z 2 -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 Z 2 -polarization in these models.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Australian National University (ANU) AU Australia (AU) University of Victoria (UVic) CA Canada (CA)

How to cite

APA:

Carey, A.L., Phillips, J., & Schulz-Baldes, H. (2019). Spectral flow for skew-adjoint Fredholm operators. Journal of Spectral Theory, 9(1), 137-170. https://dx.doi.org/10.4171/JST/243

MLA:

Carey, Alan L., John Phillips, and Hermann Schulz-Baldes. "Spectral flow for skew-adjoint Fredholm operators." Journal of Spectral Theory 9.1 (2019): 137-170.

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