A renormalisation group derivation of the overlap formulation

Starting from the continuum Dirac operator, I construct a renormalisation group blocking which transforms the continuum action into a lattice action, and I specifically consider the Wilson and overlap formalisms. For Wilson fermions the inverse blocking is non-local and thus invalid. However, I proceed to demonstrate that it is possible to construct a valid, local, blocking which, though dependent on the lattice spacing, generates the lattice overlap fermion action from the continuum action. Using this renormalisation group blocking for overlap fermions, I re-derive the Ginsparg-Wilson equations and the lattice chiral symmetry, and show that the standard Ginsparg-Wilson relation is not the most general way of expressing chiral symmetry on the lattice, nor, for overlap fermions, the most natural. I suggest how this reformulation of the Ginsparg-Wilson relation combined with the renormalisation group formulation of overlap fermions could allow the construction of a CP invariant lattice chiral gauge theory.