Harmonic scale transformation in effective QFTs with underlying structures

New equations governing the scale transformation behaviors of a QFT with underlying structures is derived and they are valid for all QFTs (with whatever renormalizability). These equations, with their several equivalent versions, can yield some new and significant insights and results that are difficult to see in the conventional renormalization programs. Among the several equivalent versions, one is similar to the usual Callan-Symanzik equation and renormalization group equation but with different meanings. From another version, the anomalous equation of energy-momentum tensor trace can be easily obtained. It can shown that with the new versions one could partially fix the scheme dependence and hence some renromalization schemes like momentum space subtractions are questionable. The classical results like asymptotic freedom are reproduced and some related issues are discussed. Finally the decoupling theorem a la Appelquist and Carrazone are discussed within our strategy. PACS number(s): 11.10.-z; 11.10.Hi; 11.10.Gh 0∗ E-mail:[email protected]