Basis Light-Front Quantization Approach to Positronium

TL;DR

This paper applies the Basis Light-Front Quantization method to positronium, developing an effective interaction in the lowest Fock sector, and finds the resulting spectrum aligns well with non-relativistic expectations.

Contribution

It introduces the first application of BLFQ to a self-bound quantum system, constructing a two-body effective interaction for positronium and analyzing its spectrum.

Findings

Spectrum agrees with Bohr model predictions

Dependence of results on theory regulators analyzed

Effective interaction captures key features of positronium

Abstract

We present the first application of the recently developed Basis Light-Front Quantization (BLFQ) method to self-bound systems in quantum field theory, using the positronium system as a test case. Within the BLFQ framework, we develop a two-body effective interaction, operating only in the lowest Fock sector, that implements photon exchange, neglecting fermion self-energy effects. We then solve for the mass spectrum of this interaction at the unphysical coupling $\alpha=0.3$. The resulting spectrum is in good agreement with the expected Bohr spectrum of non-relativistic quantum mechanics. We examine in detail the dependence of the results on the regulators of the theory.