Quantum electrodynamics of relativistic bound states with cutoffs

TL;DR

This paper analyzes a quantum electrodynamics Hamiltonian with cutoffs, proving it is self-adjoint and possesses a ground state for small coupling, advancing understanding of relativistic bound states.

Contribution

It establishes the self-adjointness and existence of a ground state for a relativistic QED Hamiltonian with cutoffs, a novel rigorous result.

Findings

Hamiltonian is self-adjoint under specified conditions

Existence of a ground state for small coupling constants

Rigorous mathematical foundation for relativistic bound states

Abstract

We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.