A renormalisation group derivation of the overlap formulation
arXiv:0903.5521 · doi:10.1016/j.nuclphysb.2009.08.016
Abstract
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 derive the Ginsparg-Wilson equations and the lattice chiral symmetry. I suggest how the construction of a lattice chiral gauge theory could follow naturally from this approach.
v4: 39 pages, some very minor changes