Relativistic two-body system in (1+1)-dimensions

TL;DR

This paper analyzes the relativistic two-body problem in (1+1)-dimensional quantum electrodynamics, deriving an effective Schrödinger equation, exploring metastable states, and discussing self-interaction effects.

Contribution

It introduces a reduction of the two-body eigenvalue problem to a one-dimensional Schrödinger-type equation with an energy-dependent potential, including delta and inverted oscillator components.

Findings

Derived conditions for metastable energy spectra.

Estimated energies and widths of metastable levels for large masses.

Discussed the impact of self-interaction effects.

Abstract

The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an one-dimensional stationary Schr\"odinger type equation with an energy-dependent effective potential which includes the delta-functional and inverted oscillator parts. The conditions determining the metastable energy spectrum are derived, and the energies and widths of the metastable levels are estimated in the limit of large particle masses. The effects of the self-interaction are discussed.