We give here some comments about the physical dimensions of the coupling. In D dimensions, the field scales as [ A ] = [ L ( 2 − − D 2 ) ] and so the coupling must scale as [ g 2 ] = [ L ( D − − 4 ) ] . This implies that Yang–Mills theory is not renormalizable for dimensions greater than four. Furthermore, for D = 4 , the coupling is dimensionless and both the field and the square of the coupling have the same dimensions of the field and the coupling of a massless quartic scalar field theory. So, these theories share the scale invariance at the classical level.