Asymptotics of the radiation field for the massless Dirac-Coulomb system

TL;DR

This paper analyzes the long-time asymptotic behavior of solutions to the massless Dirac equation with Coulomb potential, providing explicit decay rates and expansions near null and future infinities.

Contribution

It introduces new propagation estimates near the Coulomb singularity and uses hypergeometric functions to explicitly determine decay rates, advancing understanding of Dirac-Coulomb system asymptotics.

Findings

Explicit asymptotic expansions near infinities

Decay rates characterized through hypergeometric functions

Propagation estimates near potential singularity

Abstract

We consider the long-time behavior of the massless Dirac equation coupled to a Coulomb potential. For nice enough initial data, we find a joint asymptotic expansion for solutions near the null and future infinities and characterize explicitly the decay rates seen in the expansion. This paper can be viewed as a successor to previous work on asymptotic expansions for the radiation field. The key new elements are propagation estimates near the singularity of the potential, building on work of the first author with Wunsch and an explicit calculation with hypergeometric functions to determine the rates of decay.