Dispersive estimates for the Dirac equation in an Aharonov-Bohm field

TL;DR

This paper establishes dispersive estimates such as local smoothing and Strichartz estimates for the Dirac equation influenced by an Aharonov-Bohm potential, using spectral projection techniques.

Contribution

It introduces explicit spectral projection methods to derive dispersive estimates for the Dirac equation with Aharonov-Bohm fields, advancing understanding of quantum dynamics in such potentials.

Findings

Proved local smoothing estimates for the Dirac equation with Aharonov-Bohm potential.

Established weighted Strichartz estimates in this setting.

Developed explicit spectral representation of solutions.

Abstract

We prove local smoothing and weighted Strichartz estimates for the Dirac equation with a Aharonov-Bohm potential. The proof relies on an explicit representation of the solution built in terms of spectral projections.