A renormalisation group derivation of the overlap formulation Original Research Article

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 image-invariant lattice chiral gauge theory.