The Path Integral for (1 + 1)-Dimensional QCD
We derive a path integral expression for the transition amplitude in (1 + 1)-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization1 leads to a formulation in terms of gauge invariant but curvilinear variables. Remainders of the curved space are Jacobians, an effective potential, and sign factors just as for the problem of a particle in a box. Based on this result we derive a Faddeev–Popov-like expression for the transition amplitude avoiding standard infinities that are caused by integrations over gauge equivalent configurations.

title: Fuzzy Complex Grassmannian Spaces and their Star Products
abstract: We derive an explicit expression for an associative star product on noncommutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This generalises previous results for complex projective spaces and gives a discrete approximation for the Grassmannians in terms of a non-commutative algebra, represented by matrix multiplication in a finitedimensional matrix algebra. The matrices are restricted to have a dimension which is precisely determined by the harmonic expansion of functions on the commutative Grassmannian, truncated at a finite level. In the limit of infinitedimensional matrices we recover the commutative algebra of functions on the complex Grassmannians.

title: SO(3) Versus SU(2)Lattice Gauge Theory
abstract: We consider the SO (3) lattice gauge theory at weak coupling, in the Villain action. We exhibit an analytic path in coupling space showing the equivalence of the SO (3) theory with SU (2) summed over all twist sectors. This clarifies the “mysterious phase” of SO (3). As order parameter, we consider the dual string tension or center vortex free energy, which we measure in SO (3) using multicanonical Monte Carlo. This allows us to set the scale, indicating that O(700)4 lattices are necessary to probe the confined phase. We consider the relevance of our findings for confinement in other gauge groups with trivial center.

title: Monte Carlo Overrelaxation for SU(N) Gauge Theories
abstract: The standard approach to Monte Carlo simulations of SU(N) Yang-Mills theories updates successive SU(2) subgroups of each SU(N) link. We follow up on an old proposal of Creutz, to perform overrelaxation in the full SU(N) group instead, and show that it is more efficient.

title: The ground state of three quarks
abstract: We measure the static three-quark potential in SU(3) lattice gauge theory with improved accuracy, by using all available technical refinements, including Luscher-Weisz exponential variance reduction. Together with insight gained from 3-state Potts model simulations, our results allow us to sort out the merits of the Delta- and Y-ansaetze.

title: The baryon static potential from lattice QCD
abstract: Lattice QCD simulations offer the possibility of determining the potential between three static quarks from first principles. We review the status of such simulations, and the relative standing of the two theoretical proposals for the baryonic potential: the Delta law (sum of two-body terms) and the Y law (length of three flux strings joined together at a junction). We also present new results on the leading Luscher-like corrections to the asymptotic linear potential.

title: Study of the gamma p --> pi0 pi0 p reaction with the Crystal Ball/TAPS at the Mainz
abstract: The gamma p --> pi0 pi0 p reaction has been measured from threshold to 1.4 GeV using the Crystal Ball and TAPS photon spectrometers together with the photon tagging facility at the Mainz Microtron. The experimental results include total and differential cross sections as well as specific angular distributions, which were used to extract partial-wave amplitudes. In particular, the energy region below the D13(1520) resonance was studied.

title: Helicity dependence of the gamma p -> N pi channels and multipole analysis in the Delta region
abstract: A high-quality double-polarization data set for the helicity dependence of the total and differential cross-sections for both gammap --> Npi channels in the Delta region has been obtained in the framework of the GDH experiment. The experiment, performed at the Mainz microtron MAMI, used a 4pi detection system, a circularly polarized photon beam, and a longitudinally polarized frozen-spin target. These data are included in the database to perform a multipole analysis to determine the properties of the Delta(1232)-resonance. For the resonant Delta(1232) multipoles we find a very good agreement with previous analyses, while the nonresonant ones show significant deviations.

title: Compton scattering from the free and bound proton above π-threshold
abstract: The differential cross sections for Compton scattering from the proton have been measured at MAMI with three different detector setups. There is a good agreement among all the results. The theoretical calculation based on dispersion relations shows that there is no drastic change necessary in the parameters of this approach.

title: Beam-helicity asymmetries in double-pion photoproduction off the proton.
abstract: Beam-helicity asymmetries have been measured at the MAMI accelerator in Mainz in the three isospin channels gamma[over -->]p-->pi(+)pi(0)n, gamma[over -->]p-->pi(0)pi(0)p, and gamma[over -->]p-->pi(+)pi(-)p. The circularly polarized photons, produced from bremsstrahlung of longitudinally polarized electrons, were tagged with the Glasgow magnetic spectrometer. Charged pions and the decay photons of pi(0) mesons were detected in a 4pi electromagnetic calorimeter which combined the Crystal Ball detector with the TAPS detector. The precisely measured asymmetries are very sensitive to details of the production processes and are thus key observables in the modeling of the reaction dynamics.

title: Helicity dependence of the total inclusive cross section on the deuteron
abstract: A measurement of the helicity dependence of the total inclusive photoabsorption cross section on the deuteron was carried out at MAMI (Mainz) in the energy range 200 E γ 800 MeV . The experiment used a 4 π detection system, a circularly polarized tagged photon beam and a frozen spin target which provided longitudinally polarized deuterons. These new results are a significant improvement on the existing data and allow a detailed comparison with state-of-the-art calculations.