Properties of Derivative Expansion Approximations to the Renormalization Group

Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum eld theory into a set of partial di erential equations which at xed points become non-linear eigenvalue equations for the anomalous scaling dimension . We review how these equations provide a powerful and robust means of discovering and approximating non-perturbative continuum limits. Gauge elds are brie y discussed. Particular emphasis is placed on the rôle of reparametrization invariance, and the convergence of the derivative expansion is addressed.