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 ($\theta$-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 $QCD$.Comment: Proceedings of Hadrons and Strings, invited talk given by H. Kr\"{o}ger; Text (LaTeX file), 3 Figures (ps file

Monte Carlo Hamiltonian from Stochastic Basis

In order to extend the recently proposed Monte Carlo Hamiltonian to many-body systems, we suggest to concept of a stochastic basis. We apply it to the chain of $N_s=9$ coupled anharmonic oscillators. We compute the spectrum of excited states in a finite energy window and thermodynamical observables free energy, average energy, entropy and specific heat in a finite temperature window. Comparing the results of the Monte Carlo Hamiltonian with standard Lagrangian lattice calculations, we find good agreement. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature.Comment: revised version, new figures. Text (LaTeX), 4 Figs. (eps), style fil