Scattering in a Simple 2-d Lattice Model

L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass and coupled through a 3-point term, both considered in the symmetric phase. The Monte Carlo simulation makes use of the cluster updating and reduced variance operator techniques. For the Ising system we study in particular O($a^2$) effects in the phase shift of the 2-particle scattering process.Comment: 4 p + 2 PS-figures, UNIGRAZ-UTP-21-10-9

Resonance Scattering Phase Shifts in a 2-d Lattice Model

We study a simple 2-d model representing two fields with different mass and a 3-point coupling term. The phase shift in the resonating 2-particle channel is determined from the energy spectrum obtained in Monte Carlo simulations on finite lattices. Masses and wave function renormalization constants of the fields as well as mass and width of the resonance are determined and discussed. The representation of scattering states in terms of the considered operators is analysed.Comment: 24 p + 8 PS-figures, UNIGRAZ-UTP-04-05-9

Remarks on the realization of the Atiyah-Singer index theorem in lattice gauge theory

We discuss the interplay between topologically non-trivial gauge field configurations and the spectrum of the Wilson-Dirac operator in lattice gauge theory. Our analysis is based on analytic arguments and numerical results from a lattice simulation of QED_2.Comment: Talk given at LATTICE97, 3 pages, 1 figur

Proposal for Topologically Unquenched QCD

A proposal is presented for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. Strengths and shortcomings of the method are discussed and it is argued that the approximation - though being crude - shares some qualitative aspects of full QCD which relate to the issue of chiral symmetry breaking.Comment: latex, 13pp, material rearranged and better focused, final version to appear in Phys. Rev.

Quantum Fluctuations versus Topology - a Study in U(1)_2 Lattice Gauge Theory

Using the geometric definition of the topological charge we decompose the path integral of 2-dimensional U(1) lattice gauge theory into topological sectors. In a Monte Carlo simulation we compute the average value of the action as well as the distribution of its values for each sector separately. These numbers are compared with analytic lower bounds of the action which are relevant for classical configurations carrying topological charge. We find that quantum fluctuations entirely dominate the path integral. Our results for the probability distribution of the Monte Carlo generated configurations among the topological sectors can be understood by a semi-phenomenological argument.Comment: 11 pages, 3 figure

Lattice Study of the Massive Schwinger Model with a θ\theta term under L\"uscher's "Admissibility" condition

We present a numerical study of the massive two-flavor QED in two dimensions with the gauge action proposed by L\"uscher, which allows only ``admissible'' gauge fields. We find that the admissibility condition does not allow any topology changes by the local updation in Hybrid Monte Carlo algorithm so that the configurations in each topological sector can be generated separately. By developing a new method to sum over different topological sectors, we investigate $\theta$ vacuum effects. Combining with domain-wall fermion action, we obtain the fermion mass dependence and $\theta$ dependence of the meson masses, which are consistent with the analytic results by mass perturbation in the continuum theory.Comment: 3 pages, Lattice2003(chiral

Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index Theorem. We show by explicit computation that it is possible to find an accurate approximation to the Fixed Point Dirac operator containing only very local couplings.Comment: 38 pages, LaTeX, 3 figures, uses style [epsfig], a few comments and relevant references adde

Deconfinement Transition for Quarks on a Line

We examine the statistical mechanics of a 1-dimensional gas of both adjoint and fundamental representation quarks which interact with each other through 1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when the density of fundamental quarks is small, there is a first order phase transition at a critical temperature and adjoint quark density which can be interpreted as deconfinement. When the fundamental quark density is comparable to the adjoint quark density, the phase transition becomes a third order one. We formulate a way to distinguish the phases by considering the expectation values of high winding number Polyakov loop operators.Comment: Reported problems with figures fixed; 38 pages, LaTeX, 5 figures, epsfi

Linking the chiral and deconfinement phase transitions

We show that the electric glueball becomes critical at the end-point of the deconfinement phase transition in finite temperature QCD. Based on this observation and existing lattice data, we argue that the chiral phase transition at a zero quark mass and the deconfinement phase transition at an infinite quark mass are continuously connected by the glueball-sigma mixing.Comment: 4 pages, terminology corrected. To appear in Phys. Rev.

Form factors in lattice QCD

Lattice simulations of QCD have produced precise estimates for the masses of the lowest-lying hadrons which show excellent agreement with experiment. By contrast, lattice results for the vector and axial vector form factors of the nucleon show significant deviations from their experimental determination. We present results from our ongoing project to compute a variety of form factors with control over all systematic uncertainties. In the case of the pion electromagnetic form factor we employ partially twisted boundary conditions to extract the pion charge radius directly from the linear slope of the form factor near vanishing momentum transfer. In the nucleon sector we focus specifically on the possible contamination from contributions of higher excited states. We argue that summed correlation functions offer the possibility of eliminating this source of systematic error. As an illustration of the method we discuss our results for the axial charge, gA, of the nucleon.Comment: 16 pages, 11 figures, presented at Conclusive Symposium, CRC443, "Many-body structure of strongly interacting systems", 23-25 Feb 2011, Mainz, German