 Canonical normalization of a scalar gradient term

For a statistical scalar theory with gradient coefficient $K/2>0$, this rescaling gives a canonical $(\nabla \psi {)}^2/2$ term. A mass coefficient $r$ becomes $r/K$, a quartic coefficient $g$ becomes $g/K^2$, and a source $h$ becomes $h/\sqrt{K}$. Thus the simple propagator denominator $p^2+R$ and loop-coupling formulas assume these normalized coefficients. The associated measure Jacobian is field independent and belongs to the free-energy normalization.