2,431 research outputs found

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

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    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

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

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    We compute the ratio ΛL/ΛMSˉ\Lambda_L/\Lambda_{\bar{MS}} between the scale parameter ΛL\Lambda_L, associated with a lattice formulation of QCD using the overlap-Dirac operator, and ΛMSˉ\Lambda_{\bar{MS}} of the MSˉ\bar{\rm MS} renormalization scheme. To this end, the necessary one-loop relation between the lattice coupling g0g_0 and the coupling renormalized in the MSˉ\bar{{\rm MS}} scheme is calculated, using the lattice background field technique.Comment: 11 pages, 2 figure

    The California deposit rate mystery

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    Bank deposits ; Interest ; Banks and banking - California ; California

    An alternative to domain wall fermions

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    We define a sparse hermitian lattice Dirac matrix, HH, coupling 2n+12n+1 Dirac fermions. When 2n2n 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 HH 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

    Bounds on the Wilson Dirac Operator

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    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

    Topological Phases in Neuberger-Dirac operator

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    The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter m0m_0 in the Wilson-Dirac fermion operator DwD_w which enters DD through the unitary operator V=Dw(DwDw)1/2V = D_w (D_w^{\dagger} D_w)^{-1/2}. We classify the topological phases of DD by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise

    Considerations on Neuberger's operator

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    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

    Noncompact chiral U(1) gauge theories on the lattice

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    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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