Light-front two-dimensional QED: Self-field approach

TL;DR

This paper develops a self-field approach to analyze bound states in light-front two-dimensional QED with massive matter, deriving and solving the relativistic bound state equation and exploring the mass spectrum.

Contribution

It introduces a composite matter field and formulates the bound state equation including self-potential, providing solutions for the mass spectrum in both massive and massless cases.

Findings

Eigenfunctions and mass spectrum for massive matter fields obtained.

Explicit mass spectrum derived for massless matter fields.

Bound state equations incorporating self-field effects formulated.

Abstract

The self-field approach to quantum electrodynamics (QED) is used to study the bound state problem in light-front two-dimensional QED with massive matter fields. A composite matter field describing bound states is introduced and the relativistic bound state equation for the composite field including a self-potential is obtained. The Hamiltonian form of the bound state equation in terms of the invariant mass squared operator is given. The eigenvalue problem of this operator is solved for a fixed value of the self-potential, the corresponding eigenfunctions and the mass spectrum are found. In the case of massless matter fields, there are no self-field terms in the bound state equation, and the invariant mass spectrum can be evaluated explicitly. Possible ways of deriving more complete information about the bound state spectrum are briefly discussed.