Abstract
We consider the semiclassical Dirac operator coupled to a magnetic potential on a large class of manifolds, including all metric contact manifolds. We prove a sharp 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.
Citation
Nikhil Savale. "Koszul complexes, Birkhoff normal form and the magnetic Dirac operator." Anal. PDE 10 (8) 1793 - 1844, 2017. https://doi.org/10.2140/apde.2017.10.1793
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