Koszul complexes, Birkhoff normal form and the magnetic Dirac operator

Savale, Nikhil

doi:10.2140/apde.2017.10.1793

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Koszul complexes, Birkhoff normal form and the magnetic Dirac operator

Nikhil Savale

Vol. 10 (2017), No. 8, 1793–1844

DOI: 10.2140/apde.2017.10.1793

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

Vol. 10, No. 8, 2017