Abelian renormalization was accomplished independently by Julian Schwinger (1918-1994), Richard Feynman (1918-1988 ), and Sin-itiro Tomonaga (1906-1979) circa 1948. For Their monumental achievements of solving the problem of mathematical-physical infinities by sweeping them under the rug, they shared the Nobel Prize for Physics in 1965. http://nobelprize.org/nobel_prizes/physics/laureates/1965/ . For non-Abelian renormalization, the next under the carpet sweepers are Gerardus’t Hooft (born 1946) and Martinus J. G. Veltman (born 1931). Both shared the Nobel Prize for Physics in 1999.http://nobelprize.org/nobel_prizes/p...aureates/1999/

Mathematically speaking, an equivalent form of renormalization is the mathematical process of rationalization. This process requires that all variables in the rational equation given by ����=��-��, that is �� and ��, must both be rational numbers and without giving any meaning to their physical dimensions. On the other hand, if physical dimensions are considered, for example, the physical dimension of mass or the physical dimension of electric charge, then the mathematical requirement is a simple normalizing factor on the right-hand side of the rational equation such that ����=(��-��)�� where ��=1 for any specified physical dimension. If �� and �� are given in grams mass then ��=1 gram. If �� and �� are given in coulombs electric charge then ��=1 coulomb. If �� and �� are given in joules energy then ��=1 joule. This normalizing factor gives correct dimensional analysis without sacrificing the general covariance of the given rational equation. Moreover, the singular Abelian solution is given as ��=0 and ��=0 where ��=�� is implied. However, the non-Abelian solution is given by ��=-2 and ��=2 such that ����=-4 and ��-��=-4, since if ��=2 and ��=-2 then ����=-4 but ��-��=4 and therefore ����≠��-��. The first singular solution implies all the zero mass elementary particles: photons, gravitons, and gluons and the validity of Mach Principle for the concept of inertia. The non-Abelian solution implies the asymmetry of particles and antiparticles in a singular adiabatic participatory universe.