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 $α=0.3$. 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.

Figures and discussion have been extended to reflect additional calculations