  We explore the first stage of the Symanzik improvement program for lattice
Dirac fermions, namely the construction of doubler-free, highly improved
classical actions on isotropic as well as anisotropic lattices (where the
temporal lattice spacing, a_t, is smaller than the spatial one). Using field
transformations to eliminate doublers, we derive the 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) errors. Besides allowing the simulation of heavy
quarks within a relativistic framework, anisotropic lattices alleviate
potential problems due to unphysical branches of the quark dispersion relation
(which are generic 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 future steps in the
improvement program.
