Basis light-front quantization approach to positronium

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 nonrelativistic quantum mechanics. We examine in detail the dependence of the results on the regulators of the theory.