Note on a Positronium Model from Flow Equations in Front Form Dynamics

TL;DR

This paper develops a method using front-form dynamics and flow equations to analytically simplify and numerically solve for the positronium mass spectrum, showing promising cutoff dependence properties.

Contribution

It introduces a novel approach combining flow equations with front-form dynamics to analytically simplify the positronium problem.

Findings

Effective Hamiltonian obtained and spectrum computed numerically.

Results show encouraging cutoff dependence properties.

Analytical integration over azimuthal angle simplifies calculations.

Abstract

In this note we address the problem of solving for the positronium mass spectrum. We use front-form dynamics together with the method of flow equations. For a special choice of the similarity function, the calculations can be simplified by analytically integrating over the azimuthal angle. One obtains an effective Hamiltonian and we solve numerically for its spectrum. Comparing our results with different approaches we find encouraging properties concerning the cutoff dependence of the results.