CrasyDSE: A framework for solving Dyson–Schwinger equations☆
Dyson–Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automating parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automation based on a C++ code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson–Schwinger equations needs to be automated, we defer this task to a Mathematica notebook. We illustrate the complete workflow with an example from Yang–Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang–Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with DoFun, a program for the derivation of Dyson–Schwinger  Program summary  CrasyDSE  AEMY _v1_0  http://cpc.cs.qub.ac.uk/summaries/AEMY_v1_0.html  CPC Program Library, Queen’s University, Belfast, N. Ireland  Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 49030 No. of bytes in distributed program, including test data, etc.: 303958  tar.gz  Mathematica 8 and higher, C++.  All on which Mathematica and C++ are available.  All on which Mathematica and C++ are available (Windows, Unix, Mac OS).  11.1, 11.4, 11.5, 11.6.  Solve (large) systems of Dyson–Schwinger equations numerically.  Create C++ functions in Mathematica to be used for the numeric code in C++. This code uses structures to handle large numbers of Green functions.  Provides a tool to convert Mathematica expressions into C++ expressions including conversion of function names.  Depending on the complexity of the investigated system solving the equations numerically can take seconds on a desktop PC to hours on a cluster.

title: The infrared behavior of Landau gauge Yang–Mills theory in d=2, 3 and 4 dimensions
abstract: We develop a general power counting scheme for the infrared limit of Landau gauge SU ( N ) Yang–Mills theory in arbitrary dimensions. Employing a skeleton expansion, we find that the infrared behavior is qualitatively independent of the spacetime dimension d . In the cases d = 2 , 3 and 4 even the quantitative results for the infrared exponents of the vertices differ only slightly. Therefore, corresponding lattice simulations provide interesting qualitative information for the physical case. We furthermore find that the loop integrals depend only weakly on the numerical values of the IR exponents.

title: Spurious divergences in Dyson-Schwinger equations
abstract: A bstractWe revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its Dyson-Schwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green’s functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

title: On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory
abstract: A bstractWe solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.

title: Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
abstract: The low momentum behavior of the Landau gauge Gribov-Zwanziger action is investigated using the respective Dyson-Schwinger equations. Because of the mixing of the gluon and the auxiliary fields four scenarios can be distinguished for the infrared behavior. Two of them lead to inconsistencies and can be discarded. Another one corresponds to the case where the auxiliary fields behave exactly like the Faddeev-Popov ghosts and the same scaling relation as in standard Landau gauge, {kappa}{sub A}+2{kappa}{sub c}=0, is valid. Even the parameter {kappa} is found to be the same, 0.595. The mixed propagators, which appear, are suppressed in all loops, and their anomalous infrared exponent can also be determined. A fourth case provides an even stricter scaling relation that includes also the mixed propagators, but possesses the same qualitative feature, i.e. the propagators of the Faddeev-Popov ghost and the auxiliary fields are infrared enhanced and the mixed and the gluon propagators are infrared suppressed. In this case the system of equations to obtain the parameter {kappa} is nonlinear in all variables.

title: Going beyond the propagators of Landau gauge Yang-Mills theory
abstract: We present results for the propagators and the ghost-gluon vertex of Landau gauge Yang-Mills theory obtained from Dyson-Schwinger equations. Solving these three quantities simultaneously constitutes a new step in truncating these equations. We also introduce a new model for the three-gluon vertex that is motivated by lattice results. It features a zero crossing which is confirmed a posteriori by a Dyson-Schwinger calculation. Within our setup we can reproduce lattice data very well. We establish that also for the ghost-gluon vertex a difference between decoupling and scaling solutions is present. For the scaling solution we discuss the possibility of modifying the infrared exponents via an angle dependence of the ghost-gluon vertex. However, no such dependence is found in our calculations. Finally, we calculate the Schwinger function for the gluon propagator.

title: Light echoes from ancient supernovae in the Large Magellanic Cloud
abstract: The light from historical supernovae could in principle still be visible as scattered-light echoes centuries after the explosion. The detection of light echoes could allow us to pinpoint the supernova event both in position and age and, most importantly, permit the acquisition of spectra to determine the ‘type’ of the supernova centuries after the direct light from the explosion first reached Earth. Although echoes have been discovered around some nearby extragalactic supernovae, targeted searches have not found any echoes in the regions of historical Galactic supernovae. Here we report three faint variable-surface-brightness complexes with high apparent proper motions pointing back to three of the six smallest (and probably youngest) previously catalogued supernova remnants in the Large Magellanic Cloud, which are believed to have been thermonuclear (type Ia) supernovae. Using the distance and apparent proper motions of these echo arcs, we estimate ages of 610 and 410 years for two of them.

title: The FSVS Cluster Catalogue: galaxy clusters and groups in the Faint Sky Variability Survey
abstract: We describe a large sample of 598 galaxy clusters and rich groups discovered in the data of the Faint Sky Variability Survey (FSVS). The clusters have been identified using a fully automated, semiparametric technique based on a maximum likelihood approach applied to Voronoi tessellation, and enhanced by colour discrimination. The sample covers a wide range of richness, has a density of ∼28 clusters deg -2 , and spans a range of estimated redshifts of 0.05 0.6, the catalogue contributes substantially to the current total of optically selected, intermediate-redshift clusters, and complements the existing, usually X-ray selected, samples. The FSVS fields are accessible for observation throughout the whole year, making them particularly suited for large follow-up programmes. The construction of this FSVS Cluster Catalogue completes a fundamental component of our continuing programmes to investigate the environments of quasars and the chemical evolution of galaxies. We publish here the list of all clusters with their basic parameters, and discuss some illustrative examples in more detail. The full FSVS Cluster Catalogue, together with images and lists of member galaxies etc., will be issued as part of the 'NOAO (National Optical Astronomy Observatories) data products', and accessible at http://www.noao.edu/dpp/. We describe the format of these data and access to them.

title: Photon and pion scattering on the basis of quark models
abstract: Within the framework of constituent quark models of simple and complex hadrons it is possible to investigate the interrelations of scattering observables and dynamical assumptions about the underlying quark structure of the participating hadrons. In the case of simple hadrons, here baryons, the inclusion of the coupling of bound q3-states to meson-baryon decay channels, accounts for the full complexity of the fact that all excited baryonic states are in fact resonances. We present here such a description of the baryonic excitation spectrum within the non-relativistic quarkmodel with all terms of the Fermi-Breit interaction. In this case the very hadronic vertices that are responsible for the dressing of hadrons also provide a semi realistic description of various scattering observables for pion scattering and photo-production of pions. The treatment of more complex hadronic systems within the framework of a quark shell model of nuclei is then used to investigate the role of the quark Pauli principle in intermediate energy excitations of nuclei with pionic or photonic probes.

title: Pionic resonance fluorescence

title: Experimental realization of decoherence-free subspace in neutron interferometry.
abstract: A decoherence-free subspace (DFS) is an important class of quantum-error-correcting (QEC) codes that have been proposed for fault-tolerant quantum computation. The applications of QEC techniques, however, are not limited to quantum-information processing (QIP). Here we demonstrate how QEC codes may be used to improve experimental designs of quantum devices to achieve noise suppression. In particular, neutron interferometry is used as a test bed to show the potential for adding quantum error correction to quantum measurements. We built a five-blade neutron interferometer that incorporates both a standard Mach-Zender configuration and a configuration based on a DFS. Experiments verify that the DFS interferometer is protected against low-frequency mechanical vibrations. We anticipate these improvements will increase the range of applications for matter-wave interferometry.