ar X iv : h ep - l at / 9 90 90 59 v 2 2 O ct 1 99 9

ar X iv : h ep - l at / 9 91 00 40 v 1 2 5 O ct 1 99 9 RUHN - 99 - 3 The Overlap Dirac Operator ⋆

This introductory presentation describes the Overlap Dirac Operator, why it could be useful in numerical QCD, and how it can be implemented.

ar X iv : h ep - l at / 9 90 60 01 v 1 1 J un 1 99 9 1 On the I = 2 channel π - π interaction in the chiral limit ∗

An approximate local potential for the residual π + – π + interaction is computed. We use an O(a 2) improved action on a coarse 9 3 × 13 lattice with a ≈ 0.4fm. The results present a continuation of previous work: Increasing the number of gauge configurations and quark propagators we attempt extrapolation of the π + – π + potential to the chiral limit.

ar X iv : h ep - l at / 9 90 91 10 v 2 1 7 D ec 1 99 9 1 Improved

Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which O(a 2) errors are removed is presented. O(a 2) improvement of the gauge fixing condition displays the secondary benefit of reducing the size of higher-order errors. These results emphasise the importance of implementing an improved gauge fixing condition.

ar X iv : h ep - p h / 97 10 22 9 v 1 2 O ct 1 99 7 SLAC - PUB - 7663 October 1997 Z ′ INVESTIGATIONS AT FUTURE LEPTON

ar X iv : h ep - l at / 9 90 91 10 v 1 1 4 Se p 19 99 1 Improved Landau Gauge Fixing and Discretisation Errors ∗

Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which O(a 2) errors are removed is presented. O(a 2) improvement of the gauge fixing condition displays the secondary benefit of reducing the size of higher-order errors. These results emphasise the importance of implementing an improved gauge fixing condition.