A renormalisation group derivation of the overlap formulation

Details A renormalisation group derivation of the overlap formulation A renormalisation group derivation of the overlap formulation

2009-03-31

arxiv.org/abs/0903.5521v4

Nucl.Phys.B824:42-84,2010

Physics

High Energy Physics

High Energy Physics - Lattice

v4: 39 pages, some very minor changes

Scientific paper

10.1016/j.nuclphysb.2009.08.016

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.

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