Improved lattice Hamiltonians

Since the inception of lattice gauge theory much effort has been devoted to constructing improved actions. This has enabled calculations with relatively large lattice spacing a to be performed. In contrast, attempts to improve the Hamiltonian formulation of lattice gauge theory have only recently begun. Using the transfer matrix method or a Legendre transformation, improved Hamiltonians have been derived from improved actions. Here we present an alternative method. We demonstrate that direct classical improvement of the Hamiltonian is possible by modifying the electric field on the lattice. Improvement is achieved by fixing the electric field so that no O(a2) corrections appear in the kinetic Hamiltonian