Tricks to implement the overlap Dirac operator

I present several tricks to help implement the overlap Dirac operator numerically.Comment: 3 pages, latex, espcrc2.st

Alternative to Domain Wall Fermions

An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain wall fermions will in general be associated with a condition number that is of the same order of magnitude as the {\it product} of the condition number of the linear problem in the physical dimensions by the inverse bare quark mass. Thus, the computational cost of implementing true domain wall fermions using a single conjugate gradient algorithm is of the same order of magnitude as that of implementing the overlap Dirac operator directly using two nested conjugate gradient algorithms. At a cost of about a factor of two in operation count it is possible to make the memory usage of direct implementations of the overlap Dirac operator independent of the accuracy of the approximation to the sign function and of the same order as that of standard Wilson fermions.Comment: 7 pages, 1 figure, LaTeX, uses espcrc2, reference adde

Lattice Chirality

The external fermion propagator and the internal fermion propagator in the overlap are given by different matrices. A generic problem (formulated by Pelissetto) faced by all chiral, non-local, propagators of Rebbi type is avoided in this manner. Nussinov-Weingarten-Witten mass inequalities are exactly preserved. It is sketched how to obtain simple lattice chiral Yukawa models and simple expressions for covariant currents. Going beyond my oral presentation, I have added to the write-up several comments on Niedermayer's talk. His transparencies are available on the internet.Comment: LATTICE98(chiral

Wavelets and Lattice Field Theory

When continuous fields are expanded in a wavelet basis, a D-dimensional continuum action becomes a (D+1)-dimensional lattice action on the naively discretized Poincare-patch coordinates of an Euclidean AdS(D+1). New possible criteria for acceptable actions open up.Comment: 7 pages. Contribution to Lattice2017, 18-24 June, Granada, Spai

Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relate the light fermion field and the fermion field described by the truncated overlap Dirac operator and to understand the chiral property of the light fermion through the exact chiral symmetry based on the Ginsparg-Wilson relation.Comment: 35 pages, LaTeX2e, references added and updated, minor correction

Ginsparg-Wilson relation with R=(a \gamma_5 D)^{2k}

The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$ with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is constructed. It is shown that this sequence of topologically-proper lattice Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This suggests that the locality of a lattice Dirac operator is irrelevant to its index.Comment: 4 pages, 1 EPS figure, talk presented at Lattice'00 (Chiral Fermion