Abstract by Tyler Kharazi
Solving the Full Quantum Electrodynamic Hamiltonian
Quantum field theory describes the interaction of subatomic particles. The theory is known for it's accuracy and success in describing the dynamics of elementary particles. Recent work by Glasgow, Smith, Ware, et al gave a non-perturbative approach in time-resolved quantum field theory, and showed their methods in the Hamiltonian of Quantum Electrodynamics. Their work, however, only considered a subspace of QED where only one electron and one photon were considered, causing the Coulomb potential to become trivial. In this presentation we will extend the results of the previous authors to consider a field theory including electrons, positrons, and photons, a problem not yet solved exactly. However, introducing these new terms causes the Coulomb potential to play an essential role in the dynamics of the system. We analyze the Coulomb potential and discuss our methods in working towards a projection onto a 1+1D subspace of the full field theory.