Mass-shell applications of the renormalization group with arbitrary interpolating fields

The use of renormalization-group techniques to study the high-energy, fixed-angle behavior of on-shell S-matrix elements is discussed and reconciled with the fact that the field operator associated with an external on-shell particle is not unique. It is shown that, in a theory with an ultraviolet-stable fixed point, the various choices of interpolating field all give the same effective fixed-point anomalous dimension. The remaining differences in the renormalization-group equations for vertex functions of different interpolating fields are absorbed by the finite renormalization necessary for constructing properly normalized scattering amplitudes