IMPROVING LATTICE QUARK ACTIONS

We explore the first stage of the Symanzik improvement program for lat tice Dirac fermions, namely the construction of doubler-free, highly i mproved classical actions on isotropic as well as anisotropic lattices (where the temporal lattice spacing, a(t), is smaller than the spatia l one). Using field transformations to eliminate doublers, we derive t he previously presented isotropic D234 action with O(a(3)) errors, as well as anisotropic D234 actions with O(a(4)) or O(a(t)(3), a(4)) erro rs. Besides allowing the simulation of heavy quarks within a relativis tic framework, anisotropic lattices alleviate potential problems due t o unphysical branches of the quark dispersion relation (which are gene ric to improved actions), facilitate studies of lattice thermodynamics , and allow accurate mass determinations for particles with bad signal /noise properties, like glueballs and P-state mesons. We also show how field transformations can be used to completely eliminate unphysical branches of the dispersion relation. Finally, we briefly discuss futur e steps in the improvement program. (C) 1997 Elsevier Science B.V.