Self-field QED(1+1) with massless matter fields: Two-body problem

TL;DR

This paper solves the relativistic two-body problem in (1+1)-dimensional QED with massless matter fields, providing exact solutions and demonstrating equivalence of two variational formulations.

Contribution

It introduces two formulations of the two-body problem in self-field QED(1+1) and proves their equivalence, offering an exact solution in the massless case.

Findings

Both formulations yield the same spectrum.

Exact solution of the two-body relativistic equation in massless QED(1+1).

The spectrum is fully characterized.

Abstract

We consider two-body problem in the self-field (1+1)-dimensional quantum electrodynamics on the circle. We present two formulations of the problem which correspond to two different types of variational principles and prove that both formulations lead to the same spectrum of the two-body Hamiltonian with massless matter fields. We give the exact and complete solution of the relativistic two-body equation in the massless case.