Starting from the cutoff version of a field-theoretical Hamiltonian derived from an SU(n) YangMills theory in the Coulomb gauge, we investigate the structure of the emerging many-body problem within a Bogoliubov approximation for the ground state (= physical vacuum) and by considering suitable quasiparticle excitations for glueball states. The idea of the formation of a bag can be incorporated into this scheme. The energy expectation values are approximated by a cluster expansion. The (formal) results, allowing the numerical computation of the glueball spectrum at a later stage, are presented and the emerging structure is discussed. Special attention is hereby paid to the slgnificance of the Gribov ambiguity and to the consequences of the singularity of the Hamiltonian at the Gribov horizon. It is suggested that the possibility of a rising potential between gluons be ~nvestigat-ed, as such a potential could be a signal of confinement.

Lepage's improvement scheme is a recent major progress in lattice QCD, allowing to obtain continuum physics on very coarse lattices. Here we discuss improvement in the Hamiltonian formulation, and we derive an improved Hamiltonian from a lattice Lagrangian free of O(a 2 ) errors. We do this by the transfer matrix method, but we also show that the alternative via Legendre transformation gives identical results. We consider classical improvement, tadpole improvement and also the structure of Lüscher-Weisz improvement. 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.

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The coupled cluster method has been applied to the eigenvalue problem lattice Hamiltonian QCD (without quarks) for SU(2) gauge fields in two space dimensions.Using a recently presented new formulation and the truncation prescription of Guo et al. we were able to compute the ground state and the lowest 0 + -glueball mass up to the sixth order of the coupled cluster expansion.The results show evidence for a "scaling window" (i.e. good convergence and constance of dimensionless quantities) around β = 4/g 2 ≈ 3.A comparison of our results to those of other methods is presented.