Large-scale quantization of trace I: Finite propagation operators
K-Theory and Homology
2025-07-11 v3 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Operator Algebras
Abstract
Inspired by parallel developments in coarse geometry in mathematics and exact macroscopic quantization in physics, we present a family of general trace formulae which are universally quantized and depend only on large-scale geometric features of the input data. They generalize, to arbitrary dimensions, formulae found by Roe in his partitioned manifold index theorem, as well as the Kubo and Kitaev formulae for 2D Hall conductance used in physics.
Keywords
Cite
@article{arxiv.2506.10957,
title = {Large-scale quantization of trace I: Finite propagation operators},
author = {Matthias Ludewig and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:2506.10957},
year = {2025}
}
Comments
60 pages, 3 figures. Subsection 2.6 replaced by Remark 5.15