Towards Highly Improved Quark Actions

We describe two ideas useful in the construction of highly improved quark actions for simulations on coarse lattices: (i) Field transformations solve the doubler problem without destroying tree-level improvement for onor off-shell quantities. The simplest example is the Sheikholeslami-Wohlert (clover) action. Going to the next order of improvement yields the class of D234 actions. (ii) Anisotropic lattices with at < as are useful because they push up the energy of unphysical branches of the dispersion relation (which are generic to highly improved actions), allow accurate mass determinations for particles with bad signal/noise properties (glueballs, P-state mesons), and enable one to simulate heavy quarks within a relativistic framework. We present first simulation results for the quenched light hadron and charmonium spectra obtained with a D234 action on anisotropic lattices.