Confining potential under the gauge field condensation in the SU(2) Yang-Mills theory

QǬ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci-Ferrari type, the possibility of a gluon condensation ⟨Aμ+ Aμ−⟩ in low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales rc and ˜R0. The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.

Modeling Uncertainty in the Wings Method Using Interval Arithmetic

This paper introduces a novel approach to support decision-making by combining the Weighted Influence Nonlinear Gauge System (WINGS) method with interval arithmetic. This approach allows to include uncertain judgments and/or different opinions in a decision process. Our research aims at increasing the ability of WINGS to model decisions in situations of uncertainty and at extending the reach of its practical applications. The new, relatively simple and transparent method can become a useful and practical tool for the decision makers. Mathematical correctness of the proposed methodology is proven. Based on the new method, a procedure for solving a complex decision problem is created. Its applicability is illustrated by two case studies. Choosing the best option for the organization’s competitive position in a health-care organization shows how the proposed method works with uncertain judgments. Its usefulness for group decision-making is illustrated by applying it to a decision concerning allocation of public funds for sport development in a small commune.

Evaluation of the Impact of Strategic Offers on the Financial and Strategic Health of the Company—A Soft System Dynamics Approach

When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be based on rationality and the characteristics of the system being modeled. Such an approach implies the use of an appropriate analysis and modeling method. Since the majority of relationships in the model are described using the experts’ tacit knowledge, methods known as “soft” are more suitable than “hard” in those situations. Fuzzy cognitive mappings (FCM) are therefore commonly used as a technique for participatory modeling of the system, where stakeholders can convey their knowledge to the model of the system in question. In this study, we introduce a novel approach: the extended weighted influence nonlinear gauge system (WINGS), which may equally well be applied to the decision problems of this type. Appraisal of high-value and long-term offers in the sector of the telecommunication supplier industry serves as a real-world case study for testing the new method. A comparison with FCM provides a deeper understanding of the similarities and differences of the two approaches.

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born–Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein–Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as [Formula: see text]. The maximum value of the electric field increases with increasing the nonlinear parameter [Formula: see text] or decreasing the dilaton coupling [Formula: see text] and is shifted to the singularity in the absence of either dilaton field ([Formula: see text]) or nonlinear gauge field ([Formula: see text]).

Vacuum structure and gravitational bags produced by metric-independent space–time volume-form dynamics

We propose a new class of gravity-matter theories, describing [Formula: see text] gravity interacting with a nonstandard nonlinear gauge field system and a scalar “dilaton,” formulated in terms of two different non-Riemannian volume-forms (generally covariant integration measure densities) on the underlying space–time manifold, which are independent of the Riemannian metric. The nonlinear gauge field system contains a square-root [Formula: see text] of the standard Maxwell Lagrangian which is known to describe charge confinement in flat space–time. The initial new gravity-matter model is invariant under global Weyl-scale symmetry which undergoes a spontaneous breakdown upon integration of the non-Riemannian volume-form degrees of freedom. In the physical Einstein frame we obtain an effective matter-gauge-field Lagrangian of “k-essence” type with quadratic dependence on the scalar “dilaton” field kinetic term [Formula: see text], with a remarkable effective scalar potential possessing two infinitely large flat regions as well as with nontrivial effective gauge coupling constants running with the “dilaton” [Formula: see text]. Corresponding to each of the two flat regions we find “vacuum” configurations of the following types: (i) [Formula: see text] and a nonzero gauge field vacuum [Formula: see text], which corresponds to a charge confining phase; (ii) [Formula: see text] (“kinetic vacuum”) and ordinary gauge field vacuum [Formula: see text] which supports confinement-free charge dynamics. In one of the flat regions of the effective scalar potential we also find: (iii) [Formula: see text] (“kinetic vacuum”) and a nonzero gauge field vacuum [Formula: see text], which again corresponds to a charge confining phase. In all three cases, the space–time metric is de Sitter or Schwarzschild–de Sitter. Both “kinetic vacuums” (ii) and (iii) can exist only within a finite-volume space region below a de Sitter horizon. Extension to the whole space requires matching the latter with the exterior region with a nonstandard Reissner–Nordström–de Sitter geometry carrying an additional constant radial background electric field. As a result, we obtain two classes of gravitational bag-like configurations with properties, which on one hand partially parallel some of the properties of the solitonic “constituent quark” model and, on the other hand, partially mimic some of the properties of MIT bags in QCD phenomenology.