On the Spectral Analysis of Quantum Electrodynamics with Spatial Cutoffs. I

TL;DR

This paper analyzes the spectral properties of a quantum electrodynamics model with spatial cutoff, establishing self-adjointness, existence of a unique ground state under certain conditions, and properties of spectral scattering.

Contribution

It proves the Hamiltonian's self-adjointness and the existence of a unique ground state in QED with spatial cutoff, under infrared regularity.

Findings

Hamiltonian is self-adjoint

Unique ground state exists for small coupling constants

Spectral gap is closed and asymptotic fields exist

Abstract

In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground state for sufficiently small values of coupling constants. The spectral scattering theory is studied as well and it is shown that asymptotic fields exist and the spectral gap is closed.