Comparison of mass renormalization schemes for simple model systems

We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete example of bosonic quadratic and also quartic interactions. The results are compared with those obtained by the standard renormalization technique based on a spectral analysis of the usual field-based propagators. We also discuss a potential method for renormalizing a quantum field theory in a non-perturbative way using computational methods.