Abstract
We consider the energies of the one-particle states of relativistic quantum field theories in old-fashioned perturbation theory, and treat their regularization and renormalization from a strictly Hamiltonian perspective. We show that the one-loop diagrams lead to the renormalization of the mass for bosons and fermions identically to covariant perturbation theory, provided an appropriate regularization scheme is used. In particular, we show that a naive spatial momentum cutoff breaks covariance (in the limit where the cutoff is removed) in the case of the one-fermion states.
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