A General Dixmier Trace Formula for the Density of States on Open Manifolds
Mathematical Physics
2024-01-18 v2 Other Condensed Matter
Functional Analysis
Metric Geometry
math.MP
Spectral Theory
Abstract
We give an abstract formulation of the Dixmier trace formula for the density of states. This recovers prior versions and allows us to provide a Dixmier trace formula for the density of states of second order elliptic differential operators on manifolds of bounded geometry satisfying a certain geometric condition. This formula gives a new perspective on Roe's index on open manifolds.
Keywords
Cite
@article{arxiv.2304.13272,
title = {A General Dixmier Trace Formula for the Density of States on Open Manifolds},
author = {Eva-Maria Hekkelman and Edward McDonald},
journal= {arXiv preprint arXiv:2304.13272},
year = {2024}
}