Vacuum energy-density in quantum electrodynamics

The vacuum energy-density E in quantum electrodynamics is studied by renormalization group techniques as well as a diagrammatic analysis is carried out to investigate the dependence of E on an ultraviolet cut-off as the latter is led to become large. The study corresponds to the situation of finite electrodynamics with the renormalized fine-structure constant α fixed in te sense of the renormalization group. In this case explicit statements about the problem at hand may be made. In passing a study of the so-called second Leendre transform method for electrodynamics is given in an appendix. (author)