  Different decompositions of the nucleon mass, in terms of the masses and
energies of the underlying constituents, have been proposed in the literature.
We explore the corresponding sum rules in quantum electrodynamics for an
electron at one-loop order in perturbation theory. To this end we compute the
form factors of the energy-momentum tensor, by paying particular attention to
the renormalization of ultraviolet divergences, operator mixing and scheme
dependence. We clarify the expressions of all the proposed sum rules in the
electron rest frame in terms of renormalized operators. Furthermore, we
consider the same sum rules in a moving frame, where they become energy
decompositions. Finally, we discuss some implications of our study on the mass
sum rules for the nucleon.
