The condition det ( E i , j ) = 0 for a nontrivial solution gives an equation between the space dimensions, and this determines the upper critical dimension d u (provided there is only one variable dimension d in the Lagrangian). A redefinition of the coordinates and fields now shows that determining the scaling exponents N is equivalent to a dimensional analysis with respect to the wavevector k , with all coupling constants occurring in the Lagrangian rendered dimensionless. Dimensionless coupling constants are the technical hallmark for the upper critical dimension.