Perfect actions: insights in the lattice fermion problem

A revamping of the standard renormalization group approaches leads to an explicit expression of lattice formulations for arbitrary bilinear fermion actions, which can be further exploited to define new improvement methods and Chiral Gauge Theories on the lattice. In this setup the statement can be made that any fermionic action can be considered to be a Ginsparg-Wilson action or even a Perfect Action, with all associated consequences conserved. Here we present the formalism and a simple example in d = 2