We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of renormalisation in this approach. We then review the current status of studies of Abelian gauge theories [e.g., strong coupling quantum electrodynamics] before turning our attention to the non-Abelian gauge theory of the strong interaction, quantum chromodynamics. We discuss confinement, dynamical chiral symmetry breaking and the application and contribution of these techniques to our understanding of the strong interactions. KEYWORDS confinement of quarks and gluons; dynamical chiral symmetry breaking; Dyson-Schwinger equations; hadrons; quantum electrodynamics; quantum chromodynamics.

We present an unquenched calculation of the quark propagator in Landau gauge with 2+1 flavors of dynamical quarks. We use configurations generated with an improved staggered ("Asqtad") action by the MILC collaboration. This quark action has been seen to have excellent rotational symmetry and scaling properties in the quenched quark propagator. Quenched and dynamical calculations are performed on a 20 3 × 64 lattice with a nominal lattice spacing of a = 0.125 fm. The matched quenched and dynamical lattices allow us to investigate the relatively subtle sea quark effects, and even in the quenched case the physical volume of these lattices gives access to lower momenta than our previous study. We calculate the quark mass function and renormalization function for a variety of valence and sea quark masses.

No abstract

By combining the constraints of charge symmetry with new chiral extrapolation techniques and recent low mass lattice QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet, we obtain a precise determination of the strange magnetic moment of the proton. The result, namely G s M = −0.046 ± 0.019 µN , is consistent with the latest experimental measurements but an order of magnitude more precise. This poses a tremendous challenge for future experiments.

The complete tensor structure of the quark-gluon vertex in Landau gauge is determined at two kinematical points ('asymmetric' and 'symmetric') from lattice QCD in the quenched approximation. The simulations are carried out at β = 6.0, using a meanfield improved Sheikholeslami-Wohlert fermion action, with two quark masses ∼ 60 and 115 MeV. We find substantial deviations from the abelian form at the asymmetric point. The mass dependence is found to be negligible. At the symmetric point, the form factor related to the chromomagnetic moment is determined and found to contribute significantly to the infrared interaction strength.