Symmetries of discontinuous flows and the dual Rankine–Hugoniot conditions in fluid dynamics
It has recently been shown that the maximal kinematical invariance group of polytropic fluids, for smooth subsonic flows, is the semidirect product of SL  (2,  R ) and the static Galilei group G . This result purports to offer a theoretical explanation for an intriguing similarity, that was recently observed, between a supernova explosion and a plasma implosion. In this paper we extend this result to discuss the symmetries of discontinuous flows, which further validates the explanation by taking into account shock waves, which are the driving force behind both the explosion and implosion. This is accomplished by constructing a new set of Rankine–Hugoniot conditions, which follow from Noether’s conservation laws. The new set is dual to the standard Rankine–Hugoniot conditions and is related to them through the SL  (2,  R ) transformations. The entropy condition, that the shock needs to satisfy for physical reasons, is also seen to remain invariant under the transformations.

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: 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: 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: 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: 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: 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: 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: Study of the $\gamma p -> \eta p$ reaction with the Crystal Ball detector at the Mainz Microtron(MAMI-C)
abstract: Here we correct a factor of 2 missed in one of figures and the corresponding sentence in the text. It does not change any conclusions.