Transfinite harmonization by taking the dissonance out of the quantum field symphony

Particle physics may be likened to a magnificent symphony. Alas due to some instrumental defects, wrong reading of the notes and a lack of virtuosity of some members of the orchestra, a non-negligible number of dissonants are making it sound less than perfect. By means of the specific example of renormalization groups applied to GUT unification, the present work aims at illustrating the point we just made and showing how a simplictic transfinite adjustment of our formulas lead to harmonization and consequently considerable simplification of well known theories which goes as far as facilitating the discovery of new connections and the solution of many problems which were previously thought very hard, if at all possible, to solve.