Towards a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory

We develop a consistent approach to Hamiltonian lattice gauge theory, using the maximal-tree gauge. The various constraints are discussed and implemented. An independent and complete set of variables for the colourless sector is determined. A general scheme to construct the eigenstates of the electric energy operator using a symbolic method is described. It is shown how the one-plaquette problem can be mapped onto a N-fermion problem. Explicit solutions for U(1), SU(2), SU(3), SU(4), and SU(5) lattice gauge theory are shown.