Solutions of the Ginsparg-Wilson Relation

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13

A New Layer Casting System for Ceramic Laser Rapid Prototyping Apparatus

In the existing Ceramic Laser Fusion system, slurry is fed on the high temperature surface of the green part; therefore, a part of water infiltrates into the green block and vaporizes before the process of layer casting. As a result, the slurry viscosity rises gradually; the quality of the layer surface is not uniform, and the green part density is uneven. The aim of present study is to develop a new layer casting system which can solve the problems mentioned above to obtain a green part with uniform surface quality and density, and to shorten the time-taken of part fabrication. The first part of the paper illustrates the major requirements and parameters of a slurry distributor; the second part describes the integration of the slurry feeding device and layer casting system. The integrated system can feed slurry and cast thin layer simultaneously; consequently, the drawbacks of the existing system can be eliminated and the time-taken of the layer casting can be shortened. A variable-frequency drive (inverter) is used to control the motor speed. The relation between the frequency and the slurry delivery can be included in the process control program to adjust the quantity in accordance with the layer thickness; hence, the waste of the slurry can be reduced.Mechanical Engineerin

Rephasing invariance and the neutrino mu-tau symmetry

The vacuum neutrino mixing is known to exhibit an approximate $\mu-\tau$ symmetry, which was shown to be preserved for neutrino propagating in matter. This symmetry reduces the neutrino transition probabilities to very simple forms when expressed in a rephasing invariant parametrization introduced earlier. Applications to long baseline experiments are discussed.Comment: 12 pages, 4 figure

Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that is: (a) ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation), (d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change

A note on Zolotarev optimal rational approximation for the overlap Dirac operator

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w (H_w^2)^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to $(H_w^2)^{-1/2}$, one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.Comment: 23 pages, 5 eps figures, v2:minor clarifications, and references added, to appear in Phys. Rev.