Renormalization-group transformation
= Renormalization-group transformation
{title2=$g'=R_b(g)$}
A renormalization-group transformation integrates out selected short-distance degrees of freedom and restores chosen cutoff and field-normalization conventions. It defines a map $R_b$ on couplings at a length factor $b$. Its discrete <Jacobian matrix> multipliers differ from <eigenvalues> of the generator of a continuous <renormalization-group flow>; the relation for a scaling direction is $\lambda=b^y$.