We address an old problem in lattice gauge theory - the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge theory. We test the method by computing the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian of this theory and compare them with analytical results. We observe a reasonable scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.

We address an old problem in lattice gauge theory — the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. Using the method of Monte Carlo with importance sampling, we construct a stochastic basis of Bargmann link states, drawn from a physical probability density function. In the next step, we compute transition amplitudes between stochastic basis states. Then, we extract energy spectra and wave functions from a matrix of transition elements. To test this method, we apply it to U(1) lattice gauge theory in (2+1) dimensions and compute the energy spectrum, wave functions and thermodynamic functions of the electric Hamiltonian of this theory. We compare the numerical results with the analytical results and observe a reasonable scaling of energies and wave functions in the variable of time.

We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization.

We demonstrate that front form quantisation with periodicity in a compact light-like direction (discretized light-cone quantisation) violates microcausality.

We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization. We present numerical results for the mass spectrum of the vector and scalar particle. We find good agreement with chiral perturbation theory in the strong coupling regime and also with other non-perturbative studies (Hamer et al. [Phys. Rev. D 56 (1997) 55], Mo and Ferry [J. Comput. Phys. 108 (1993) 159]) in the non-relativistic regime. The most important new result is the study of the theta-action, and computation of vector and scalar masses as a function of the theta-angle. We find excellent agreement with chiral perturbation theory. Finally, we give results for the distribution functions. We compare our results with Bergknoffs variational study from the infinite momentum frame in the chiral region. (C) 1998 Published by Elsevier Science B.V. All rights reserved.

We suggest a new Hamiltonian lattice approach, using a regularisation motivated by deep inelastic scattering. We discuss the relation between distribution functions and the F1 structure function. We have tested the method by computing the critical behaviour of the scalar model and find agreement with scaling behaviour and with results by Lüscher and Weisz.

We suggest a Hamiltonian formulation on a momentum lattice using a physically motivated regularization using the Breit frame which links the maximal parton number to the lattice size. This scheme restricts parton momenta to positive values in each spatial direction. This leads to a drastic reduction in the number of degrees of freedom as compared to a regularization in the rest frame (center at zero momentum). We discuss the computation of physical observables such as (i) the mass spectrum in the critical region, (ii) structure and distribution functions, (iii) the S matrix, and (iv) finite temperature and finite density thermodynamics in the Breit-frame regularization. For the scalar (3+1)-dimensional phi(4) theory we present numerical results for the mass spectrum in the critical region. We observe scaling behavior for the mass of the ground state and for some higher-lying states. We compare our results with renormalization group results by Luscher and Weisz. Using the Breit frame we calculate, for QCD, the relation between the W-mu upsilon tensor, structure functions (polarized and unpolarized), and quark distribution functions. We use the improved parton model with a scale dependence and take into account a nonzero parton mass. In the Bjorken limit we find the standard relations between F-1, F-2, g(1), and the quark distribution, functions. We discuss the role of helicity. We present numerical results for parton distribution functions in the scalar model. For the phi(4) model we find no bound state with internal parton structure.