Radiation fields for semilinear Dirac equations with spinor null forms

TL;DR

This paper develops a radiation field framework for semilinear Dirac equations with spinor null forms, establishing a nonlinear isomorphism between initial data and radiation fields to advance scattering theory.

Contribution

It introduces radiation fields for semilinear Dirac equations with spinor null forms and proves a nonlinear isomorphism linking initial data to radiation fields.

Findings

Defined radiation fields for the equations.

Established a nonlinear isomorphism.

Analyzed linear Dirac radiation fields.

Abstract

Inthispaper,weinvestigatethescatteringtheoryofhalf-spinwavesthroughtheuse of radiation fields. We define the radiation fields for semilinear Dirac equations with spinor null forms and establish a nonlinear isomorphism between the weighted energy space of initial data and the weighted energy space of radiation fields. The proof relies on a detailed examination of the linear Dirac radiation fields and the use of a suitable functional framework.