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We perform numerical studies of the running coupling constant α R (p 2 ) and of the gluon and ghost propagators for pure SU (2) lattice gauge theory in the minimal Landau gauge. Different definitions of the gauge fields and different gauge-fixing procedures are used respectively for gaining better control over the approach to the continuum limit and for a better understanding of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex renormalization constant is finite in the continuum limit, confirming earlier results by all-order perturbation theory. In the low momentum regime, the gluon form factor is suppressed while the ghost form factor is divergent. Correspondingly, the ghost propagator diverges faster than 1/p 2 and the gluon propagator appears to be finite. Precision data for the running coupling α R (p 2 ) are obtained. These data are consistent with an IR fixed point given by lim p→0 α R (p 2 ) = 5(1).

In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behaviour of the propagators are changed substantially. We find the very intriguing result that the gluon propagator vanishes in the infrared exactly like p 2 , whilst the ghost propagator is exactly as singular as 1/p 4 . We also find that the value of the infrared fixed point of the QCD coupling is much decreased from the y-max estimate: it is now equal to 4π/3. Schwinger equations for the gluon and ghost form factors F and G. The approximations were two-fold: firstly the vertices were taken bare, and secondly angular averaging was introduced (the so-called y-max approximation). Deferring to later work an improvement of the vertices, in this paper we seek to remove the deficiency of the y-max approximation. On the one hand the results might be regarded simply as quantitative adjustments to the y-max calculations; but on the other hand they are far from negligible. The numerical value of the infrared fixed point is reduced by a factor of almost three; and the finding that the gluon propagator has a simple zero, while the ghost propagator has a double pole, might perhaps be deemed a qualitatively new result.As an improvement on the y-max approximation used in Ref.[2], we now solve the coupled integral equations for the gluon and ghost propagators with an exact treatment of the angular 1 atkinson@phys.rug.nl 2 bloch@phys.rug.nl 1

We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer γ5-hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of nonhermitian chiral random matrix theory for both trivial and nontrivial topology.PACS numbers: 12.38. Gc, 02.10.Yn Recent years have seen great advances in two areas that at first sight seem to be totally unrelated: (i) the study of nonhermitian operators in the natural sciences [1] and (ii) the problem of chiral symmetry on the lattice [2]. In this article we focus on a problem in which both of these areas are relevant, namely quantum chromodynamics (QCD) at nonzero baryon (or quark) density, which is important for the study of relativistic heavy-ion collisions, neutron stars, and the early universe [3].If a quark chemical potential µ is added to the QCD Dirac operator, the operator loses its hermiticity properties and its spectrum moves into the complex plane. This causes a variety of problems, both analytically and numerically. Lattice simulations are the main source of nonperturbative information about QCD, but at µ = 0 they cannot be performed by standard importance sampling methods because the measure of the Feynman path integral, which includes the complex fermion determinant, is no longer positive definite. While a generic solution to this so-called sign problem is unlikely to be found [4], a number of recent works have been able to make progress by circumventing the problem in various ways [5,6,7]. These methods all agree on the transition temperature from the hadronic to the quark-gluon phase in the regime µ/T 1 [3].A better analytical understanding of QCD at very high baryon density has been obtained by a number of methods [8], and the QCD phase diagram has been studied in model calculations based on symmetries [9]. Chiral random matrix theory (RMT) [10], which makes exact analytical predictions for the correlations of the small Dirac eigenvalues, has been extended to µ = 0 [11], and a mechanism was identified [12] by which the chiral condensate at µ = 0 is built up from the spectral density of the Dirac operator in an extended region of the complex plane, in stark contrast to the Banks-Casher mechanism at µ = 0.A first comparison of lattice data with RMT predictions at µ = 0 was made in Ref.[13] using staggered fermions. One issue with staggered fermions is that the topology of the gauge field is only visible in the Dirac spectrum if the lattice spacing is small and various improvement and/or smearing schemes are applied [14]. To avoid these issues, we would like to work with a Dirac operator that implements a lattice version of chiral symmetry and has exact zero modes at finite lattice spacing. The overlap operator [15] satisfies these requirements at µ = 0. In the following, we show how the overlap operato...

A recent claim that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson-Schwinger equations are taken to be bare. The running coupling is shown to be uniquely determined by the equations and to have a large finite infrared limit.

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period pl . Allowing for collisions, these oscillations are damped on a time scale r determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless r ӷ pl and pl ϳ1/⌳ QCD ϳ1 fm/c. ͓S0556-2821͑99͒06123-8͔

We employ a bispinor gap equation to study superfluidity at nonzero chemical potential: µ = 0, in two-and three-colour QCD. The two-colour theory, QC2D, is an excellent exemplar: the order of truncation of the quark-quark scattering kernel: K, has no qualitative impact, which allows a straightforward elucidation of the effects of µ when the coupling is strong. In rainbow-ladder truncation, diquark bound states appear in the spectrum of the three-colour theory, a defect that is eliminated by an improvement of K. The corrected gap equation describes a superfluid phase that is semi-quantitatively similar to that obtained using the rainbow truncation. A model study suggests that the width of the superfluid gap and the transition point in QC2D provide reliable quantitative estimates of those quantities in QCD.

Abstract. The proton's elastic electromagnetic form factors are calculated using an Ansatz for the nucleon's Poincaré covariant Faddeev amplitude that only retains scalar diquark correlations. A spectator approximation is employed for the current. On the domain of q 2 accessible in modern precision experiments these form factors are a sensitive probe of nonperturbative strong interaction dynamics. The ratio of Pauli and Dirac form factors can provide realistic constraints on models of the nucleon and thereby assist in developing an understanding of nucleon structure.