Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality

TL;DR

This paper investigates the scattering behavior of large initial data in Hartree-type nonlinear Dirac equations with Yukawa potential, leveraging charge conjugation and chirality-induced null structures to establish results.

Contribution

It introduces a novel approach using charge conjugation and chirality to prove scattering for large data in nonlinear Dirac equations.

Findings

Established scattering for large data with small charge conjugation component.

Utilized null structure induced by chirality to handle nonlinear interactions.

Extended understanding of scattering phenomena in Dirac equations with Yukawa potential.

Abstract

We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential derived from pseudoscalar field. We establish scattering for large data but with a relatively small part of initial data associated with charge conjugation by exploiting null structure induced by chirality.