New Computational method for solving the time-based Dirac Equation

Current computational methods for the Dirac equation are prone to negative behavior such as fermion doubling, instability, and poor performance for low-mass particles. These issues are usually addressed by artificial stabilizers and careful after-simulation tuning but this may cast doubt on the physical accuracy of computational results. We show that our space-time finite element method for the time-based Dirac equation converges to analytic solutions without artificial stabilization or after-simulation tuning even in the low-mass regime. This method may be an important tool for simulating partially understood particles such as neutrinos where low-mass performance is essential and after-simulation tuning is inappropriate.