EXPLICIT SOLUTIONS FOR THE THOOFT TRANSFORMATION

The 't Hooft transformation is a change of variables of the renormalized coupling constant to a new coupling parameter such that the resulting Gell-Mann-Low (GML) function is a low-order polynomial with coefficients independent of renormalization scheme. Explicit expressions for this transformation are given for (4)d, d=2,3,4, field theories, QED, and quantum chromodynamics. The solutions are expressed in terms of the original GML function (g) and their properties are given in some detail. In several cases these transformations are shown to be valid up to the first nontrivial zero of (g). © 1979 The American Physical Society.