Koszul complexes, Birkhoff normal form and the magnetic Dirac operator

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.

References in corpus (2)

• Magnetic Wells in Dimension Three
• A semi-classical trace formula at a non-degenerate critical level

Cited by in corpus (3)

• Sub-leading asymptotics of ECH capacities
• A Gutzwiller type trace formula for the magnetic Dirac operator
• Hyperbolicity, irrationality exponents and the eta invariant