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We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion species of identical mass. In the simulation we are using Wilson fermions where chiral symmetry is explicitly broken. Since there is no known simple order parameter it is non-trivial to identify the critical line of the chiral phase transition. We therefore need to find observables which allow an identification of a possible restoration of chiral symmetry. We utilize the PCAC-relations in order to identify the critical coupling, where chiral symmetry is restored., Comment: 3 pages (LaTeX), 4 figures (EPS)

The Schwinger model, defined in the space interval $-L \le x \le L$, with (anti)periodic boundary conditions, is canonically quantized in the light-cone gauge $A_-=0$ by means of equal-time (anti)commutation relations. The transformation diagonalizing the complete Hamiltonian is explicitly constructed, thereby giving spectrum, chiral anomaly and condensate. The structures of Hilbert spaces related both to free and to interacting Hamiltonians are completely exhibited. Besides the usual massive field, two chiral massless fields are present, which can be consistently expunged from the physical space by means of a subsidiary condition of a Gupta-Bleuler type. The chiral condensate does provide the correct non-vanishing value in the decompactification limit $L \to \infty$., Comment: CERN-TH/97-164, 35 pages, revTeX, no figures

We investigate the interplay between topological charge and the spectrum of the fermion matrix in lattice QED(2) using analytic methods and Monte Carlo simulations with dynamical fermions. A new theorem on the spectral decomposition of the fermion matrix establishes that its real eigenvalues (and corresponding eigenvectors) play a role similar to the zero eigenvalues (zero- modes) of the Dirac operator in continuous background fields, Using numerical techniques we concentrate on studying the real part of the spectrum. These results provide new insights into the behavior of physical quantities as a function of the topological charge, In particular we discuss the fermion determinant, the effective action and pseudoscalar densities.

22 pp. (1996)., A general method is presented that allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the spatio-temporal scale. Particles that are confined to small scales, i.e. do not appear in the physical spectrum, can be uncovered in this way without taking recourse to gauge fields or indefinite metric spaces. In this way notions such as quark, gluon, colour symmetry and confinement acquire a new and intrinsic meaning which is stable under gauge or duality transformations. The method is illustrated by the example of the Schwinger model.

11 pp. (1995)., We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly.

Confinement properties of the 1+1 Schwinger model can be studied by computing the string tension between two charges. It is finite (vanishing) if the fermions are massive (massless), corresponding to the occurrence of confinement (screening). Motivated by the possibility of experimentally simulating the Schwinger model, we investigate here the robustness of its screened and confined phases. First, we analyze the effect of nearest-neighbor density-density interaction terms, which—in the absence of the gauge fields—give rise to the Thirring model. The resulting Schwinger-Thirring model (very often also referred to as the gauged Thirring model) is studied, also in presence of a topological θ-term, showing that the massless (massive) model remains screened (confined) and that there is deconfinement only for θ=±π in the massive case. Estimates of the parameters of the Schwinger-Thirring model are provided with a discussion of a possible experimental setup for its realization with ultracold atoms. The possibility that the gauge fields live in higher dimensions while the fermions remain in 1+1 is also considered. One may refer to this model as the pseudo-Schwinger-Thirring model. It is shown that the screening of external charges occurs for 2+1 and 3+1 gauge fields, exactly as it occurs in 1+1 dimensions, with a radical change of the long distance interaction induced by the gauge fields. The massive (massless) model continues to exhibit confinement (screening), signaling that it is the dimensionality of the matter fields, and not of the gauge fields, to determine confinement properties. A computation for the string tension is presented in perturbation theory. Our conclusion is that 1+1 models exhibiting confinement or screening—massless or massive, in the presence of a topological term or not—retain their main properties when the Thirring interaction is added or the gauge fields live in a higher dimension.