Vol. 10, No. 8, 2017

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Koszul complexes, Birkhoff normal form and the magnetic Dirac operator

Nikhil Savale

Vol. 10 (2017), No. 8, 1793–1844
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.

Keywords
Dirac operator, Weyl law, eta invariant
Mathematical Subject Classification 2010
Primary: 35P20, 81Q20
Secondary: 58J40, 58J28
Milestones
Received: 1 October 2015
Revised: 19 May 2017
Accepted: 20 June 2017
Published: 18 August 2017
Authors
Nikhil Savale
Department of Mathematics
University of Notre Dame
Notre Dame, IN
% 46556
United States