Spectral flow for real skew-adjoint Fredholm operators
| Title: | Spectral flow for real skew-adjoint Fredholm operators |
|---|---|
| Authors: | Carey, Alan L., Phillips, John, Schulz-Baldes, Hermann |
| Publication Year: | 2016 |
| Collection: | Mathematics Mathematical Physics |
| Subject Terms: | Mathematical Physics, Mathematics - Functional Analysis |
| More Details: | An analytic definition of a $\mathbb{Z}_2$-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 $\mathbb{Z}_2$-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 $\mathbb{Z}_2$-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 $\mathbb{Z}_2$-polarization in these models. Comment: final corrections before publication in J. Spectral Theory |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1604.06994 |
| Accession Number: | edsarx.1604.06994 |
| Database: | arXiv |
| Description not available. |