Narrow Results

An attempt has been made to analyze the magnetic symmetry of the non-Abelian gauge theory associated with the strong interactions using the fibre bundle formulation. Utilizing the gauge field topology, the analysis of dual dynamics associated with the non-Abelian fields is shown to have important bearings on the nonperturbative hadronic effects like confinement of colored quarks and gluons inside hadrons. The state of dual superconductivity for the magnetically condensed vacuum has been analyzed to understand the bulk QCD magnetic properties by evaluating the current correlators in magnetic gauge in terms of the dielectric parameters. The dielectric behavior has been shown to lead to the p^-4 confining nature to the dual gluon propagators and to provide an effective macroscopic description of the complicated nonperturbative microscopic interactions of charged particles in dual QCD. The p^-4 behavior of dual gluon propagator has also been shown to confirm the linearly rising inter-quark confining potential with an explicit dual gluon mass dependency in dual QCD.

Ghost condensates of dimension two are analyzed in a class of nonlinear gauges in pure Yang–Mills theories. These condensates are related to the breaking of the SL(2, R) symmetry, present in these gauges.

The dual superconductor picture of the QCD vacuum is thought to describe the various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg–Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important feature of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen–Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

In the framework of a relativistic constituent quark model we propose some confining potentials behaving like r and r² at large distances which allow for analytical solutions of the Dirac equation. The solutions are given in explicit form.

The well-known topological monopoles originally investigated by 't Hooft and Polyakov are known to arise in classical Yang–Mills–Higgs theory. With a pure gauge theory, it is known that the classical Yang–Mills field equation do not have such finite energy configurations. Here we argue that such configurations may arise in a semi-quantized Yang–Mills theory, where the original gauge group, SU(3), is reduced to a smaller gauge group, SU(2), and with some combination of the coset fields of the SU(3) to SU(2) reduction acting as effective scalar fields. The procedure is called semi-quantized since some of the original gauge fields are treated as quantum degrees of freedom, while others are postulated to be effectively described as classical degrees of freedom. Some speculation is offer on a possible connection between these monopole configurations and the confinement problem, and the nucleon spin puzzle.

A system consisting of an ion and an electron interacting through the Hulthén potential confined in an impenetrable spherical box, with the ion at the centre is considered. Superpotential which is the crucial quantity in supersymmetric quantum mechanics is proposed for the 1s and 2p states. Variational wave functions are thence derived. Energies are calculated from these for different values of the radius of box (R) and these are compared to the exact values; good agreement is shown to exist between the two. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s→2p transition and the dipole polarizability for different values of R.

For a theory with a pseudo-scalar coupling and in the case that there is a constant electric or magnetic strength expectation value, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. While in the case of a constant electric field strength expectation value the static potential remains Coulombic, in the case of a constant magnetic field strength the potential energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static charges.

In this paper, we show a dual gauge structure in the (2+1)D fermionic-σ model. For this model, there exists a confinement–deconfinement transition between ordered state and quantum disordered state. At the quantum critical point the effective Lagrangian is reduced to the massless, non-interacting Wess–Zumino model with an N = 1 supersymmetry.

The infrared behavior of Yang–Mills theory at finite temperature provides access to the role of confinement. In this review recent results on this topic from lattice calculations and especially Dyson–Schwinger studies are discussed. These indicate persistence of a residual confinement even in the high-temperature phase. The confinement mechanism is very similar to the one in the vacuum for the chromomagnetic sector. In the chromoelectric sector screening occurs at the soft scale g²T, although not leading to a perturbative behavior.

We study the mixing of excited states of a hydrogen atom in a cavity with de-excited states plus a confined photon as a model for the coupling of quark–antiquark and quark–antiquark–gluon hybrid states in QCD. For an interesting range of parameters, the results are analytic. We find a case for which wave functions (and hence decay patterns) may be at odds with mass with respect to identification of a state as hybrid or not.

On the basis of the confinement mechanism earlier proposed by author, the electric form factor of η-meson is nonperturbatively calculated. The latter is then applied to describe electromagnetic decay η→2γ which entails estimates for parameters of the confining SU(3)-gluonic field in η-meson. The corresponding estimates of the gluon concentrations, electric and magnetic color field strengths are also adduced for the mentioned field.

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov–Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter λ equal to 1) and the minimal Coulomb gauge (corresponding to λ = 0). For small values of λ we find that the spatially-transverse gluon propagator D^tr(0, |p|), considered as a function of the spatial momenta |p|, is clearly infrared suppressed. This result is in agreement with the Gribov–Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit λ→0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (λ = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of λ.

We perform the first studies of various inter-quark potentials in SU(3)_c lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential V_3Q is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. Quark confinement mechanism in baryons is also investigated in maximally-Abelian projected QCD. We next study the multi-quark potentials V_nQ (n = 4,5) in SU(3)_c lattice QCD, and find that they are well described by the one-gluon-exchange Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks. Finally, we study the heavy-heavy-light quark (QQq) potential both in lattice QCD and in a lattice-QCD-based quark model.

At a critical finite chemical potential and low temperature QCD undergoes the chiral restoration phase transition. The folklore tradition is that simultaneously hadrons are deconfined and there appears the quark matter. We demonstrate that it is possible to have confined but chirally symmetric hadrons at a finite chemical potential and hence beyond the chiral restoration point at a finite chemical potential and low temperature there could exist a chirally symmetric matter consisting of chirally symmetric but confined hadrons. If it does happen in QCD, then the QCD phase diagram should be reconsidered with obvious implications for heavy ion programs and astrophysics.

We review a recently developed framework employing computable Renormalization Group (RG) decimations for gauge theories in the lattice regularization. They provide upper and lower bounds at every scale for free energies and some order parameters. By interpolating between these bounds representations of the exact quantities are obtained at progressively longer scales (coarser lattices). In the case of the SU(2) gauge theory in four dimensions RG flow to the confining strongly coupled regime is obtained for any initial coupling; whereas for the U(1) theory a fixed point is reached for small initial coupling.

Adopting the gauge-invariant but path-dependent variables formalism, we study the coupling of torsion fields with photons in the presence of an external background electromagnetic. We explicitly show that, in the case of a constant electric field strength expectation value, the static potential remains Coulombic, while in the case of a constant magnetic field strength expectation value a confining potential is obtained. This result displays a marked qualitative departure from the usual coupling of axionlike particles with photons in the presence of an external magnetic field.

In this work, the energy eigenvalues for the confined Lennard–Jones potential are calculated through the Variational Method allied to the Supersymmetric Quantum Mechanics. Numerical results are obtained for different energy levels, parameters of the potential and values of confinement radius. In the limit, where this radius assumes great values, the results for the non-confined case are recovered.

We review the role of zero-temperature entropy in several closely-related contexts in QCD. The first is entropy associated with disordered condensates, including . The second is effective vacuum entropy arising from QCD solitons such as center vortices, yielding confinement and chiral symmetry breaking. The third is entanglement entropy, which is entropy associated with a pure state, such as the QCD vacuum, when the state is partially unobserved and unknown. Typically, entanglement entropy of an unobserved three-volume scales not with the volume but with the area of its bounding surface. The fourth manifestation of entropy in QCD is the configurational entropy of light-particle world-lines and flux tubes; we argue that this entropy is critical for understanding how confinement produces chiral symmetry breakdown, as manifested by a dynamically-massive quark, a massless pion, and a condensate.

Although non-perturbative functional methods are often associated with low energy Quantum Chromodynamics, contemporary studies indicate that they provide reliable tools to characterize a much wider spectrum of strongly interacting many-body systems. In this paper, we aim to provide a modest overview on a few notable applications of Dyson–Schwinger equations to QCD and condensed matter physics. After a short introduction, we lay out some formal considerations and proceed by addressing the confinement problem. We discuss in some detail the heavy quark limit of Coulomb gauge QCD, in particular the simple connection between the non-perturbative Green's functions of Yang–Mills theory and the confinement potential. Landau gauge results on the infrared Yang–Mills propagators are also briefly reviewed. We then focus on less common applications, in graphene and high-temperature superconductivity. We discuss recent developments, and present theoretical predictions that are supported by experimental findings.

An extended version of four-dimensional (4D) SU(2) lattice gauge theory is considered in which different inverse coupling parameters are used, for plaquettes which are purely space-like, and β_V for those which involve the Euclidean time-like direction. It is shown that when β_H = ∞ the partition function becomes, in the Coulomb gauge, exactly that of a set of non-interacting three-dimensional (3D) O(4) classical Heisenberg models. Long range order (LRO) at low temperatures (weak coupling) has been rigorously proven for this model. It is shown that the correlation function demonstrating spontaneous magnetization in the ferromagnetic phase is a continuous function of g_H at g_H = 0 and therefore, that the spontaneously broken phase enters the (β_H, β_V) phase plane (no step discontinuity at the edge). Once the phase transition line has entered, it can only exit at another identified edge, which requires the SU(2) gauge theory within also to have a phase transition at finite β. A phase exhibiting spontaneous breaking of the remnant symmetry left after Coulomb gauge fixing, the relevant symmetry here, is non-confining. Easy extension to the SU(N) case implies that the continuum limit of zero-temperature 4D SU(N) lattice gauge theories is not confining, in other words, gluons by themselves do not produce a confinement.