Fuzzy Complex Grassmannian Spaces and their Star Products
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: Vortex free energies in SO(3) and SU(2) lattice gauge theory
abstract: Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement- deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).

title: The Quark Structure of Pentaquarks
abstract: Motivated by the possible observation of the $\Theta^+(1530)$, we study the quark structure of pentaquark states in quenched lattice QCD. The complete set of 19 local sources that have the proper symmetry for positive or negative parity isoscalar pentaquarks is constructed, as well as a nonlocal source composed of two displaced ``good'' diquarks. Quantitative structure information is determined from diagonalizing the 19-dimensional correlation matrix and from calculating the overlaps of sources with the lattice eigenstates. The volume dependence of the overlap is studied to differentiate between scattering and localized resonant states. The positive parity state has a small component of two ``good'' diquarks, and its energy is too much higher than the negative parity state to be a candidate for the $\Theta^+(1530)$.

title: Potts correlators and the static three-quark potential
abstract: We discuss the two- and three-point correlators in the two-dimensional three-state Potts model in the high temperature phase of the model. By using the form factor approach and perturbed conformal field theory methods we are able to describe both the large distance and the short distance behaviours of the correlators. We compare our predictions with a set of high precision Monte Carlo simulations (performed on the triangular lattice realization of the model) finding a complete agreement in both regimes. In particular we use the two-point correlators to fix the various non-universal constants involved in the comparison (whose determination is one of the results of our analysis) and then use these constants to compare numerical results and theoretical predictions for the three-point correlator with no free parameter. Our results can be used to shed some light on the behaviour of the three-quark correlator in the confining phase of the (2 + 1)-dimensional SU(3) lattice gauge theory which is related by dimensional reduction to the three-spin correlator in the high temperature phase of the three-state Potts model. The picture which emerges is that of a smooth crossover between a Δ-type law at short distances and a Y-type law at large distances.

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: Polyakov loop and its relation to static quark potentials and free energies
abstract: It appears well accepted in the literature that the correlator of Polyakov loops in a finite temperature system decays with the average free energy of the static quark-antiquark system and can be decomposed into singlet and adjoint (or octet for QCD) contributions. By fixing a gauge respecting the transfer matrix, attempts have been made to extract those contributions separately. In this paper we point out that the average and adjoint channels of Polyakov loop correlators are misconceptions. We show analytically that all channels receive contributions from singlet states only, and give a corrected definition of the singlet free energy. We verify this finding by simulations of the 3D SU(2) pure gauge theory in the zero-temperature limit, which allows one to cleanly extract the ground state exponents and the nontrivial matrix elements. The latter account for the difference between the channels observed in previous simulations.

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.

title: Neutron polarizabilities investigated by quasifree Compton scattering from the deuteron.
abstract: Measuring Compton scattered photons and recoil neutrons in coincidence, quasifree Compton scattering by the neutron has been investigated at MAMI (Mainz) at theta(lab)(gamma) = 136 degrees in an energy range from 200 to 400 MeV. From the data a polarizability difference of alpha(n)-beta(n) = 9.8+/-3.6(stat)+2.1-1.1(syst)+/-2.2(model) in units of 10(-4) fm(3) has been determined. In combination with the polarizability sum alpha(n)+beta(n) = 15.2+/-0.5 deduced from photoabsorption data, the first precise results for the neutron electric and magnetic polarizabilities, alpha(n) = 12.5+/-1.8(stat)+1.1-0.6(syst)+/-1.1(model) and beta(n) = 2.7-/+1.8(stat)+0.6-1.1(syst)-/+1.1(model), are obtained.

title: STATUS OF THE GDH EXPERIMENT ON THE DEUTERON AT MAMI

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: 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.