Instantons and monopoles in general Abelian gauges
A relation between the total instanton number and the quantum numbers of magnetic monopoles that arise in general Abelian gauges in SU (2) Yang-Mills theory is established. The instanton number is expressed as the sum of the `twists' of all monopoles, where the twist is related to a generalized Hopf invariant. The origin of a stronger relation between instantons and monopoles in the Polyakov gauge is discussed.

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: 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: Chiral fermions on the lattice
abstract: We discuss topological obstructions to putting chiral fermions on an even-dimensional lattice. The setting includes Ginsparg–Wilson fermions, but is more general. We prove a theorem which relates the total chirality to the difference of generalised winding numbers of chiral projection operators. For an odd number of Weyl fermions this implies that particles and anti-particles live in topologically different spaces.

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: Measurement of the helicity dependence for the gamma p -> n pi(+) channel in the second resonance region
abstract: The helicity dependence of the γp→nπ + reaction has been measured for the first time in the photon energy range from 450 to 790 MeV. The experiment, performed at the Mainz Microtron (MAMI), used a 4π-detector system, a circularly polarized, tagged photon beam, and a longitudinally polarized frozen-spin target. Although these polarized data are mainly sensitive to mechanisms involving the D 13 (1520) resonance, a cusp structure at the η production threshold can be clearly observed. These data are significantly different from the predictions of the existing multipole analyses and are used to determine the helicity amplitudes of the D 13 (1520) and S 11 (1535) resonances with improved accuracy.

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.

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: Search for the charge-conjugation-forbidden decay omega ->eta pi(0)
abstract: A new upper limit of 2.3x10(-4) on the branching ratio of the decay omega -<eta pi(0) has been obtained using the Crystal Ball multiphoton spectrometer at the Mainz Microtron MAMI. This decay is forbidden by charge-conjugation invariance of the strong and electromagnetic interactions. We have also obtained the upper limit of 2.3x10(-4) for the forbidden decay omega -< 3 pi(0) and the upper limit of 2.4x10(-4) for omega -< 2 pi(0).

title: Quasi-free Compton scattering and the polarizabilities of the neutron
abstract: Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the Göttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θLABγ = 136.2°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π+n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be αn - βn = 9.8±3.6(stat)+2.1-1.1(syst)±2.2(model) in units of [10-4]fm3. In combination with the polarizability sum αn + βn = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, αn = 12.5±1.8(stat)+1.1-0.6(syst)±1.1(model) and βn = 2.7±1.8(stat)+0.6-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ(n)π = (58.6±4.0)×10-4fm4.