Uniqueness of renormalized quantities in dimensional regularization

It is proved that in any order of perturbation expansion the dimensionally regularized Feynman integration may be multiplied by an arbitrary analytic function of the space-time dimension, which can be absorbed in the redefinition of the bare coupling constants so that the finite renormalized quantities are unchanged. It is also shown that the Ward-Takahashi identities of a gauge theory are unaffected by this multiplication factor. A most convenient choice of the multiplicative analytic function is suggested and the effective potential of massless $\lambda {\phi }^4$ theory is calculated in the two-loop approximation as an explicit example.