A Gutzwiller type trace formula for the magnetic Dirac operator

TL;DR

This paper establishes a Gutzwiller trace formula for magnetic Dirac operators on certain manifolds, linking spectral properties to Reeb orbits, and applies it to derive a semiclassical eta invariant formula.

Contribution

It introduces a novel Gutzwiller trace formula for magnetic Dirac operators on metric-contact manifolds with non-resonant Reeb flows, connecting spectral data to geometric orbits.

Findings

Trace formula involving Reeb orbits

Semiclassical limit for eta invariant

Application to metric-contact manifolds

Abstract

For manifolds including metric-contact manifolds with non-resonant Reeb ow, we prove a Gutzwiller type trace formula for the associated magnetic Dirac operator involving contributions from Reeb orbits on the base. As an application, we prove a semiclassical limit formula for the eta invariant.