Improved lattice gauge field Hamiltonian

Abstract

The improvement problem of lattice gauge field theories is discussed within the Hamiltonian formulation. For a pure gauge theory, we derive an improved quantum Hamiltonian from a lattice Lagrangian free of ${O(a}^{2})$ errors in the classical limit. We do this by the transfer matrix method, but we also show that the alternative via Legendre transformation gives identical results. The resulting color-electric energy is an infinite series, which is expected to be rapidly convergent. For the purpose of practical calculations, we construct a simpler improved Hamiltonian, which includes only nearest-neighbor interactions. We also consider tadpole improvement and the structure of L\"uscher-Weisz improvement. As a check of the improved Hamiltonian we compute the gluon dispersion relation and find that the ${O(a}^{2})$ errors disappear.