Normalized solutions for the Klein Gordon-Dirac system

TL;DR

This paper establishes the existence of stationary solutions for a coupled Klein-Gordon-Dirac system, modeling electron-photon interactions, using variational methods to find critical points of an energy functional.

Contribution

It introduces a novel variational approach to prove stationary solutions for the Klein-Gordon-Dirac system with fixed L2-norm.

Findings

Existence of stationary solutions proven

Solutions characterized as critical points of an energy functional

Method applicable to coupled quantum field systems

Abstract

We prove the existence of a stationary solution for the system describing the interaction between an electron coupled with a massless scalar field (a photon). We find a solution, with fixed $L^{2}$-norm, by variational methods, as a critical point of an energy functional.