Differential geometric invariants for time-reversal symmetric Bloch-bundles: the "Real" case
Abstract
Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related "Real" (resp. "Quaternionic") Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in [DG1] for the "Real" case and in [DG2] for the "Quaternionic" case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article (and its companion [DG3]) we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the "Real" case we generalize the Chern-Weil theory and we showed that the assignment of a "Real" connection, along with the related differential Chern class and its holonomy, suffices for the classification of "Real" vector bundles in low dimensions.
Keywords
Cite
@article{arxiv.1502.01232,
title = {Differential geometric invariants for time-reversal symmetric Bloch-bundles: the "Real" case},
author = {Giuseppe De Nittis and Kiyonori Gomi},
journal= {arXiv preprint arXiv:1502.01232},
year = {2016}
}
Comments
50 pages. key words: Topological quantum systems, Bloch-bundle, "Real and "Quaternionic" vector bundles , equivariant connections, "Real" Chern-Weil theory. (v2) Version accepted for publication on J. Math. Pays. Introduction partially rewritten. minor corrections in the main body of the text