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

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 (α = 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.

Scattering in strong electromagnetic fields: Transverse size effects in time-dependent basis light-front quantization

“…BLFQ has the advantage of being able to solve bound state problems involving positronium [37] and hadron structures [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. In this paper we follow previous work on the physical electron eigenstates in BLFQ [54].…”

Ab Initio No Core Shell Model with Leadership-Class Supercomputers

“…For example, Hamiltonian methods are gaining popularity in non-perturbative solutions of quantum field theory [32][33][34][35][36][37][38][39][40][41][42] motivated, in part, by the advances being made by our teams in solving the ab initio NCSM/NCFC. Recent applications, in what is called the Basis Light-Front Quantization (BLFQ) approach [32][33][34], include non-perturbative solutions of positronium at strong coupling [39,[43][44][45][46][47] and solutions for the mass spectra, decay constants, form factors and vector meson production rates for heavy quarkonia [48][49][50][51][52][53][54][55]. Remarkably, results for QED in the BLFQ approach have been achieved with Hamiltonian matrix dimensions exceeding 18 billion basis states [41,42].…”

Advances in Basis Light-Front Quantization

“…In the previous work we have solved this system by using an effective interaction acting only in the | eē sector [13,14]. Now we try to solve this system in QED in a basis consisting of the | eē and | eēγ two Fock sectors.…”

“…6 we also compare the ground state binding energy E b evaluated with RA from Eq. (13), to that with DA according to P − Ψ = D Ψ |P − QED | Ψ D . The convergence with respect to N max2 is improved when RA is used.…”