Improved lattice gauge field Hamiltonian - art. no. 034503.

The improvement problem of lattice gauge field theories is discussed within the Hamiltonian formulation. For a pure gauge theory, we derive an improve d quantum Hamiltonian from a lattice Lagrangian free of O(a(2)) errors in t he classical limit. We do this by the transfer matrix method, but we also s how that the alternative via Legendre transformation gives identical result s. The resulting color-electric energy is an infinite series, which is expe cted to be rapidly convergent. For the purpose of practical calculations, w e construct a simpler improved Hamiltonian, which includes only nearest-nei ghbor interactions. We also consider tadpole improvement and the structure of Luscher-Weisz improvement. As a check of the improved Hamiltonian we com pute the gluon dispersion relation and find that the O(a2) errors disappear . [S0556-2821(99)04301-5].