In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dirac operators can be derived in a similar fashion. This renormalization group transformation modifies the gauge action and adds a number of irrelevant terms to the lattice action. The procedure is not valid for lattice Dirac operators which do not exactly satisfy the Ginsparg-Wilson relation, for example the Wilson operator.
%0 Journal Article
%1 Cundy:2008cn
%A Cundy, Nigel
%D 2008
%K GinspargWilson Lattice Overlap PerfectAction Renormalisation
%T Block renormalization group transformations and overlap
fermions
%U http://www.slac.stanford.edu/spires/find/hep/www?eprint=arXiv:0810.1131
%X In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dirac operators can be derived in a similar fashion. This renormalization group transformation modifies the gauge action and adds a number of irrelevant terms to the lattice action. The procedure is not valid for lattice Dirac operators which do not exactly satisfy the Ginsparg-Wilson relation, for example the Wilson operator.
@article{Cundy:2008cn,
abstract = {In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dirac operators can be derived in a similar fashion. This renormalization group transformation modifies the gauge action and adds a number of irrelevant terms to the lattice action. The procedure is not valid for lattice Dirac operators which do not exactly satisfy the Ginsparg-Wilson relation, for example the Wilson operator. },
added-at = {2009-04-08T14:50:11.000+0200},
archiveprefix = {arXiv},
author = {Cundy, Nigel},
biburl = {https://www.bibsonomy.org/bibtex/27a3ccedacbf8637e08e69035c8506599/gber},
description = {SPIRES-HEP: FIND EPRINT ARXIV:0810.1131},
eprint = {0810.1131},
interhash = {a206a92f6f9b6dd3260cf9dd4830f4f8},
intrahash = {7a3ccedacbf8637e08e69035c8506599},
keywords = {GinspargWilson Lattice Overlap PerfectAction Renormalisation},
primaryclass = {hep-lat},
slaccitation = {%%CITATION = 0810.1131;%%},
timestamp = {2009-04-08T14:50:11.000+0200},
title = {{Block renormalization group transformations and overlap
fermions}},
url = {http://www.slac.stanford.edu/spires/find/hep/www?eprint=arXiv:0810.1131},
year = 2008
}