A Feature of the Off-Shell Renormalization Schemes in Quantum Field Theory

It is shown that the off-shell renormalization schemes for subtraction of ultraviolet divergences in Quantum Field Theory produce zero for sums of perturbative corrections to physical quantities when all perturbation orders are taken into account. That is the off-shell renor malization schemes are in this sense unphysical. In this connection it is desirable to develop on-shell renormalization schemes for different quantum theories.