Non-perturbative Calculation of the Positronium Mass Spectrum in Basis Light-Front Quantization

TL;DR

This paper presents a non-perturbative numerical method to calculate the positronium mass spectrum using basis light-front quantization, incorporating one-photon exchange but neglecting self-energy effects, and compares well with non-relativistic predictions.

Contribution

It introduces a Hamiltonian approach with an effective interaction for positronium in basis light-front quantization, improving non-perturbative spectrum calculations at strong coupling.

Findings

Mass spectrum agrees with Bohr spectrum at strong coupling

Effective Hamiltonian captures key features of positronium

Numerical diagonalization yields accurate mass eigenvalues

Abstract

We report on recent improvements to our non-perturbative calculation of the positronium spectrum. Our Hamiltonian is a two-body effective interaction which incorporates one-photon exchange terms, but neglects fermion self-energy effects. This effective Hamiltonian is diagonalized numerically in a harmonic oscillator basis at strong coupling ($\alpha=0.3$) to obtain the mass eigenvalues. We find that the mass spectrum compares favorably to the Bohr spectrum of non-relativistic quantum mechanics evaluated at this unphysical coupling.