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., Mo and Perry) in the nonrelativistic regime. The most important new result is the study of the θ-action, and computation of vector and scalar masses as a function of the θ-angle. We find excellent agreement with chiral perturbation theory. Finally, we give results for the distribution functions. We compare our results with Bergknoff's variational study from the infinite momentum frame in the chiral region.
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 of degrees of freedom compared to a regularization in the rest frame (center at zero momentum). We discuss the computation of physical observables like (i) mass spectrum in the critical region, (ii) structure and distribution functions, (iii) S-matrix, (iv) nite temperature and nite density thermodynamics in the Breit-frame regularization. For the scalar 4 3+1 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 L uscher and Weisz. Using the Breit-frame, we calculate for QCD the relation between the W 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 non-zero parton mass. In the Bjorken limes we nd the standard relations between F1, F2, g1 and the quark distribution functions. We discuss the rôle of helicity. We present numerical results for parton distribution functions in the scalar model. For the 4 -model we nd no bound state with internal parton structure. For the 3 -model we nd a distribution function with parton structure similar to Altarelli-Parisi behavior of QCD.
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 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.