Koszul complexes, Birkhoff normal form and the magnetic Dirac operator
Analysis of PDEs
2018-11-05 v1 Differential Geometry
Spectral Theory
Abstract
We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. In the absence of a Fourier integral parametrix, the method relies on the use of almost analytic continuations combined with the Birkhoff normal form and local index theory.
Keywords
Cite
@article{arxiv.1511.08545,
title = {Koszul complexes, Birkhoff normal form and the magnetic Dirac operator},
author = {Nikhil Savale},
journal= {arXiv preprint arXiv:1511.08545},
year = {2018}
}