Dimensional regularization and the renormalization group

The behaviour of a renormalized field theory under scale transformations x to lambda x; p to p/ lambda can be found in a simple way when the theory is regularized by the continuous dimension method. The techniques proposed have several applications in dimensionally regularized theories: short distance behaviour is expressed in terms of the single poles at n=4, and all coefficients in front of the higher poles 1/(n-4)/sup k/ are expressed in terms of those of the single poles 1/(n-4), without calculating any diagram. In some cases the Taylor series in 1/(n-4) can be summed, leading to some exact results for the infinities of the full theory. (7 refs).