Dynamical Confinement Research Articles

Variational approach to the QCD wave functional: Dynamical mass generation and confinement.

We perform a variational calculation in the SU(N) Yang Mills theory in 3+1 dimensions. Our trial variational states are explicitly gauge invariant, and reduce to simple Gaussian states in the zero coupling limit. Our main result is that the energy is minimized for the value of the variational parameter away form the perturbative value. The best variational state is therefore characterized by a dynamically generated mass scale $M$. This scale is related to the perturbative scale $\Lambda_{QCD}$ by the following relation: $\alpha_{QCD}(M)={\pi\over 4}{1\over N}$. Taking the one loop QCD $\beta$- function and $\Lambda_{QCD}=150 Mev$ we find (for N=3) the vacuum condensate ${\alpha\over \pi}<F^2>= 0.008 Gev^4$.

"Dynamical confinement" in neural networks and cell cycle.

In this paper randomization of well-known former mathematical models is proposed (i.e., the Hopfield model for neural networks and the Hahn model for the cell cycle) in order to facilitate the study of their asymptotic behavior: in fact, we replace the determination of the stability basins for attractors and boundaries by the study of a unique (or a small number of) invariant measure(s), whose distribution function maxima (or, respectively, percentile contour lines) correspond to the location of the attractors (or, respectively, boundaries of their stability basins). We give the name of "confinement" to this localization of the mass of the invariant measure(s). We intend to show here that the study of the confinement is in certain cases easier than the study of underlying attractors, in particular if these last are numerous and possess small stability basins (for example, for the first time we calculate the invariant measure in the random Hopfield model in a case for which the deterministic version exhibits many attractors, and in a case of phase transition). (c) 1995 American Institute of Physics.

Covariant off-shell model for dynamical quark confinement

A model for quark propagation is developed in which quarks cannot go on-shell and thus are confined dynamically. The approach is based on a recently proposed time-ordered formulation of the relativistic many-body problem made manifestly covariant by an off-shell modification of Lorentz transformations. It is argued that the present off-shell formalism is better suited for studies of dynamical confinement since it provides a straightforward off-shell extension of the Dirac equation. In the usual Lorentz-covariant formulation, by contrast, spinor solutions do not exist for quarks which cannot go on-shell. Defining the quark propagator by a nonlinear time-ordered one-gluon-loop expansion, similar to a Dyson-Schwinger equation, an energy-dependent quark mass is determined by a nonlinear self-consistency condition. The corresponding time-ordered propagator is found to possess no poles for real energies, thus ensuring confinement. Evidence is given that it is analytic in the entire upper half of the complex energy plane as required by causality. In the model, the self-energy integral exists without regularization, with the convergence being provided by the chiral limit of the quark mass itself. The self-consistency condition exhibits the scaling behavior of the renormalization group and provides an eigenvalue condition for the low-energy value of the quark-gluon coupling constant. Its numerically determined value of g 2/4π= 4.712 can actually be derived in the soft-gluon limit as g 2/4π=3/2π. Implications of these findings and possible further applications are discussed.

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

We study a model Dyson-Schwinger equation for the quark propagator closed using an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \sim q^2/[(q^2)^2 + b^4]$} and two {\it Ans\"{a}tze} for the quark-gluon vertex: the minimal Ball-Chiu and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of $b=b_c$ such that the model does not support dynamical chiral symmetry breaking for $b>b_c$. We discuss and apply a confinement test which suggests that, for all values of $b$, the quark propagator in the model {\bf is not} confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behaviour of QCD.

Nucleon form factors in a projected chiral soliton model with dynamical confinement

We calculate nucleon form factors in the framework of a chiral chromodielectric model. The model state describing the nucleon is an angular momentum and isospin eigenstate with J = T = 1 2 obtained by means of Peierls-Yoccoz projection from the hedgehog. We present results for the electromagnetic form factors and also for the axial form factors of the nucleon. There is a fairly good agreement with the data for small momentum transfers. For high momentum transfers (i.e. q 2 > 0.1 GeV 2 the agreement becomes poorer. As a general rule the calculated form factors fall too rapidly.

Dynamical confinement in bosonized two-dimensional QCD.

In the bosonized version of two dimensional theories non trivial boundary conditions (topology) play a crucial role. They are inevitable if one wants to describe non singlet states. In abelian bosonization, color is the charge of a topological current in terms of a non-linear meson field. We show that confinement appears as the dynamical collapse of the topology associated with its non trivial boundary conditions.

Pi - pi scattering in a QCD-based model field theory.

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyze the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom, and quark confinement, allows one to calculate ${f}_{\ensuremath{\pi}}$, ${m}_{\ensuremath{\pi}}$, ${r}_{\ensuremath{\pi}}$, and the partial wave amplitudes in $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies $E\ensuremath{\simeq}550$ MeV.

Nucleon description in a projected chiral soliton model with dynamical confinement

We present a nucleon description based on a chiral version of a colour-dielectric model with non-strange quarks and scalar-isoscalar (σ) and pseudoscalar-isovector ( π ) meson fields. Approximate solutions of the model are obtained in a beyond-mean-field calculation. Quarks are treated in the valence approximation, occupying the same nodeless s-orbit. Coherent states are used to describe the meson clouds. The total baryon state has a hedgehog shape. A standard projection formalism is used to obtain model states with definite angular momentum and isospin and total linear momentum zero. To a large extent we use a variation-after-projection (VAP) procedure to obtain radial amplitudes for the mesons and quarks. The model state which describes the nucleon is used for evaluating its static properties. The projection on linear momentum causes a major effect on the rest mass of the nucleon. This effect amounts to ~ 30% decrease with respect to the mean-field energy. Except for the charge radius of the proton, the other observables are less affected by the projections. We find sets of parameters for which a reasonable nucleon description is obtained.

Models of Neptune's arc rings

Incomplete arc rings have been detected in orbit about the planet Neptune. We review models that have been proposed to explain the dynamical confinement of such structures. These models are then tested against currently available observational data.

Pseudodeconfinement and dynamical confinement in the quark plasma.

We elaborate upon phenomenological models of high-temperature hadronic matter at zero baryon density. We discuss the choice of a practical set of ``fundamental'' degrees of freedom, indicate their relationship to dynamically confined plasma modes, and suggest in what way they may account for the phase transition and other thermodynamic features. We offer a partial resolution to the conflict between the requirement of dynamical confinement and the apparent thermodynamic deconfinement of the plasma. When all quark masses are large, the quarks may appear to be deconfined, even though they are technically confined.

Dynamical mass generation and confinement in two-dimensional gauge theories

Operator solutions are used to study non-perturbative aspects of two-dimensional models, with quartic fermionic interactions, internal SU( N)-flavor and SU( M) diagonal color index. The models exhibit dynamical mass generation. Bosonization aspects of the chiral SU( M) Gross-Neveu model are considered. Off-diagonal SU( M) current conservation emerges as a quantum property. Dynamical mass generation is accomplished by the appearance of M − 1 zero-mode excitations. These M − 1 “would-be” Goldstone bosons are screened by the introduction of M − 1 “gluon” fields in the “torus” of the SU( M) group. The consequent vacuum condensation of these free charges allows for 〈θ a| ΨΨ|θ a〉 ≠ 0 . As the screened charges are free, the theories decouple and no additional confinement aspects appear. However, if the gauge fields are introduced such that the screened charges are not free, then additional confinement aspects will be present. The hamiltonian term responsible for the quartic fermionic interaction and consequently for the dynamical mass generation plays, within the confinement aspects, an analogous role to that which is played by a mass term explicitly introduced in the theory. Quarks with screened “diagonal color” are liberated only for some special “θ-worlds”.

The many-body content of quantum gauge theories and spontaneous symmetry breaking

Abstract The many-body content of quantum field theories is studied by performing the limit velocity of light → ∞. It is found that the limit of the Goldstone model is the Bogoliubov model of superfluidity, and the limit of the vacuum of spontaneously broken abelian theories is a plasma whose excitations are the limit of the massive gauge bosons. The method appears suitable to study dynamical supersymmetry breaking and colour confinement.

Relativistic Hamiltonian dynamics. II. Momentum-dependent interactions, confinement and quantization

The previously developed covariant classical relativistic N-particle dynamics is extended to momentum-dependent interactions and generalized to a gauge-independent constraint reduction. This reduction is made via center-of-momentum variables as well as via the more conventional individual particle variables. A canonical quantization is then carried out. The two-body problem is discussed in detail for the case of momentum-dependent interactions. It is demonstrated that such interactions can give rise to dynamical confinement both classically and quantum mechanically. The prototype interaction − β 2( ξ · π) 2 has a harmonic oscillator type spectrum and shows a linear dependence of the binding energy on the angular momentum for small particle rest masses ( m 1, m 2 ⪡ β).