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Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator

We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the results are very promising. We also present a detailed computation of the spectrum and chiral properties of the Schwinger Model in the overlap lattice formulation.Comment: Lattice 2000 (Chiral Fermions

Noncompact chiral U(1) gauge theories on the lattice

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic phase choice can be further improved to produce a perfect phase choice, with a lattice Wess-Zumino functional that is just as simple as the one in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in PR

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Lambda-parameter of lattice QCD with the overlap-Dirac operator

We compute the ratio $\Lambda_L/\Lambda_{\bar{MS}}$ between the scale parameter $\Lambda_L$, associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{\bar{MS}}$ of the $\bar{\rm MS}$ renormalization scheme. To this end, the necessary one-loop relation between the lattice coupling $g_0$ and the coupling renormalized in the $\bar{{\rm MS}}$ scheme is calculated, using the lattice background field technique.Comment: 11 pages, 2 figure

Bounds on the Wilson Dirac Operator

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement

An alternative to domain wall fermions

We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of $H$ and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alternative to domain wall fermions in the context of numerical QCD.Comment: Revtex Latex, 26 pages, 1 figure, a few minor change

Mobius Fermions: Improved Domain Wall Chiral Fermions

A new class of domain wall fermions is defined that interpolates between Shamir's and Bori\c{c}i's form without increasing the number of Dirac applications per CG iteration. This class represents a full (real) M\"obius transformation of the Wilson kernel. Simulations on quenched Wilson lattices with $\beta = 6.0$ show that the number of lattice sites ($L_s$) in the fifth dimension can be reduced by a factor of 2 or more at fixed value of chiral symmetry violations measured by the residual mass ($m_{res}$).Comment: 3 pages, 1 figur

Considerations on Neuberger's operator

We discuss new approaches to the numerical implementation of Neuberger's operator for lattice fermions and the possible use of block spin transformations.Comment: LATTICE 99 (Improvement and Renormalization