Renormalization Conditions and the Sliding Scale in the Implicit Regularization Scheme: A Simple Connection

We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the calculation, the introduction of a mass scale is a direct consequence of a set of renormalization conditions. As an illustration the one-loop -function for QED and ⁴ theories are derived. They are given in terms of derivatives of appropriately systematized functions (related to definite parts of the amplitudes) with respect to a mass scale . Our formal scheme can be easily generalized for higher loop calculations.