Neural network approach to Dirac quantum field theory

We present a neural network-based computational method for investigating strong-field-induced electron-positron pair creation from the quantum vacuum. In computational quantum field theory (CQFT), the fermionic vacuum is modeled as the set of all negative-energy eigenstates of the Dirac equation. To compute the dynamical evolution of electronic and positronic observables, each of these Dirac sea states must be evolved in time. Traditionally, this is done by solving the time-dependent Dirac equation separately for each state---a computationally intensive task. As a first step toward addressing the runtime challenges, especially in higher-dimensional spatial calculations, we explore an alternative solution method based on neural networks. In this approach, the neural network is trained to leverage information from the time evolution of the first state, thereby significantly reducing the CPU time required to compute the time evolution of the remaining states.