English

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

Analysis of PDEs 2023-07-06 v3

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.

Keywords

Cite

@article{arxiv.2112.06111,
  title  = {Asymptotics of the radiation field for the massless Dirac-Coulomb system},
  author = {Dean Baskin and Robert Booth and Jesse Gell-Redman},
  journal= {arXiv preprint arXiv:2112.06111},
  year   = {2023}
}

Comments

50 pages, 2 figures. Version 3: minor changes to improve exposition and fix small errors, added discussion of higher-dimensional problem