2015/02/28 by Giuseppe De Nittis, Kiyonori Gomi · 18 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #Geometry #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena #cond-mat.mes-hall #math-ph #math.MP #msc:53A55 #msc:53C80 #msc:55N25 #msc:57R22
paper · pdf · doi:10.1063/1.4948742
published in Journal of Mathematical Physics 57(5) (American Institute of Physics) · 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
openalex publication_date 2016/05/01 · arxiv created 2016/05/17 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] 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 With this article and its companion [G. De Nittis and K. Gomi (unpublished)] we want to cover this gap.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 show 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.