Quark confinement and instanton-like Euclidean field configurations

We introduce the concept of “c instanton” configuration and show that the QED₂ confinement may be understood as a saturation of the functional integrals in terms of such new configuration.     

Phase transition over the gauge group center and quark confinement in QCD

A lattice gauge model with the phase transition corresponding to spontaneous breakdown of the group center symmetry is considered. The possible continuum limit in a phase with permanently confined quarks is discussed.     

A stagnant gauge for QCD

It is shown that the gauge-fixing parameter α of standard covariant gauges may legitimately be replaced by an operator α(□). In particular, α may be chosen so that the gluon propagator has a “stagnant” tensor structure proportional to g_ην for all momenta. This choice of gauge simplifies explicit calculations and leads to renormalization group equations with no $\text{?}\text{?α}$ term.     

QCD Dirac spectrum and components of the gauge field

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how a certain component of the gauge field is related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad momentum region is relevant for the low-lying Dirac spectrum and topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.     

Spaces of regular gauge field configurations on a lattice and gauge fixing conditions

We consider spaces of lattice gauge field configurations satisfying gauge invariant regularity conditions, and intersections of these spaces with a surface given by gauge fixing conditions. We prove that if these conditions are chosen properly then configurations belonging to the intersection are small and regular.Research supported in part by the National Science Foundation under Grant PHY-82-03669     

QCD axion from a higher dimensional gauge field theory

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.     

Infrared exponents and the running coupling of Landau gauge QCD and their relation to confinement

The infrared behaviour of the gluon and ghost propagators in Landau gauge QCD is reviewed. The Kugo-Ojima confinement criterion and the Gribov-Zwanziger horizon condition result from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement with corresponding lattice data obtained recently. The resulting running-coupling approaches a fix point in the infrared, . Two different fits for the scale dependence of the running coupling are given and discussed.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.Aw General properties of QCD (dynamics, confinement, etc.) - 14.70.Dj Gluons - 12.38.Lg Other nonperturbative calculations - 11.15.Tk Other nonperturbative techniques - 02.30.Rz Integral equations     

规范场和夸克动力学模型--关于QCD和层子模型的议论

文章讨论了夸克QCD模型和层子模型的关系，说明夸克动力学模型的基础是非亚贝尔规范场理论．层子模型是半唯象理论，没有动力学互作用的机制．QCD由于以非亚贝尔规范场为动力学互作用机制，在高能行为有渐近自由的重要性质．层子模型是低能束缚态的唯象性质的模型，与渐近自由是完全无关．强调“渐近自由”是一个独立于夸克模型的物理概念，它的理论基础是非亚贝尔规范场理论；当把非亚贝尔规范场作为夸克相互作用建立了夸克的动力学模型——量子色动力学（quantum chromodynamics，QCD）；层子模型是想把静态夸克模型发展为动力学模型，但它走的路线与QCD完全不同，层子的互作用不涉及非亚贝尔规范场，与渐近自由是不同概念和不同思想和不同考察区域；文章还指出夸克动力学的QCD模型同层子模型是哲学思想不同，物理思想也不相同的路线，层子模型没有接纳非亚贝尔规范场而未能达成创新的成果．文章也强调三十多年前层子模型研究的创新意识和团队精神是我们值得推崇的优秀传统．     

A gauge model with confinement in four dimensions

It is shown that the correctly written “1/k⁴” propagator in four space-time dimensions leads to a consistent pertubative expansion of a superrenormalizable (asymptotically free) abelian gauge model. Confinement is found in any order of perturbation theory. A discussion of the physical space is sketched and the violation of asymptotic completeness is pointed out.     

Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ–Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ–Lee term. We find that they cannot.     

Renormalization constant of the color gauge field as a probe of confinement

The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by where denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it. Received: 20 September 2001 / Published online: 23 November 2001     

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.     

QCD plasma parameters in axial gauge

Within the framework of imaginary time formalism we investigate the structure of the gluon polarization tensor and relate its structure functions to the dispersion relation of plasma eigenmodes. To one loop order, we calculate the transversal structure function to leading order in the high temperature expansion as well as the first subleading order contribution in the long wavelength limit. The result is used to express the dynamical mass and the damping constant for transversal plasma eigenmodes. The aim of our present paper is a systematic discussion of the gauge fixing vector dependence of the damping constant. In the limit of temporal axial gauge we encounter a negative damping constant contradicting previous results.     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

BRST invariance in Coulomb gauge QCD

In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ?²${?}^2$, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g⁴)$O\left(g^4\right)$, example.     

Some topological configurations in gauge theories

A Higgs vacuum field is characterized by the set of conditionsD =0, which lead to a generalized Meissner effect and partially determine the vector potentialA in terms of . Applying this method to the Weinberg-Salam theory, we assert that there exist stringlike configurations in which a pair of magnetic poles are bound by a flux string of theZ ⁰ field, with an energy scale in the TeV range. We also point out that pure gauges in non-Abelian gauge theories are not well-defined due to topological singularities. In order to be meaningful, they must be enlarged to a class of almost pure gauges which include the various known topological configurations.Work supported in part by the U.S. Department of Energy, San Francisco Office, and by the Sherman Fairchild Distinguished Scholars Program.On leave from the University of Chicago.