0 Why Use a Hamilton Approach in QCD ?

We discuss QCD in the Hamiltonian frame work. We treat finite density QCD in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum (θ-angles) and distribution functions in QED 1+1. We suggest a Monte Carlo method to construct low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in Hamiltonian QCD. 1. Introduction There are presently the following problems in QCD: How to compute non-perturbatively (on the lattice): (a) QCD at non-zero chemical potential-finite quark density. (b) Hadron structure functions, at small x B and small Q. (c) S-matrix, scattering cross sections, phase shifts, (d) Decay amplitudes. Here, we want to discuss recent progress in the Hamiltonian formulation, QCD at non-zero chemical potential in the strong coupling regime, distribution function in QED 1+1 , the Monte Carlo Hamiltonian, and improvement of the continuum behavior of the Hamiltonian.