Singular solutions of the Yang-Mills equations and bag models

Lunev, F. A.; Pavlovskii, O. V.

doi:10.1007/bf02557164

Cited by 6 publications

(9 citation statements)

References 26 publications

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“…69, p. 103, where the following can be adopted: F µν n ν = 0 for gauge fields; and ψ = 0 for quark fields. As a problem in bubble dynamics, one uses − ¼F µν F µν = ΣJ −1 ∇ ν (Jn ν ) + B for a quark current J and surface tension Σ. Alternatively the more recent Lunev-Pavlovsky bag with a singular Yang-Mills solution on the bag surface [70][71][72][73] can be utilized (also probably eliminating the need for ε(σ) in (23), a point that is yet to be addressed). interior solution is depicted as a many-bag problem using a Swiss-cheese (modified Einstein-Straus) model with zero pressure on the bag surfaces.…”

Section: Characterizing Scalar-tensor Gravity and Hadronsmentioning

confidence: 99%

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A New Strategy for Solving Two Cosmological Constant Problems in Hadron Physics

Wilson¹

2013

JMP

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A new approach to solving two of the cosmological constant problems (CCPs) is proposed by introducing the AbbottDeser (AD) method for defining Killing charges in asymptotic de Sitter space as the only consistent means for defining the ground-state vacuum for the CCP. That granted, Einstein gravity will also need to be modified at short-distance nuclear scales, using instead a nonminimally coupled scalar-tensor theory of gravitation that provides for the existence of QCD's two-phase vacuum having two different zero-point energy states as a function of temperature. Einstein gravity alone cannot accomplish this. The scalar field will be taken from bag theory in hadron physics, and the origin of the bag constant B is accounted for by gravity's CC as Bag

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Section: Characterizing Scalar-tensor Gravity and Hadronsmentioning

confidence: 99%

“…interior solution is depicted as a many-bag problem using a Swiss-cheese (modified Einstein-Straus) model with zero pressure on the bag surfaces. Applicable boundary conditions are in [69][70][71][72][73].…”

Section: Characterizing Scalar-tensor Gravity and Hadronsmentioning

confidence: 99%

A New Strategy for Solving Two Cosmological Constant Problems in Hadron Physics

Wilson¹

2013

JMP

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“…The choice of the subtraction term ǫ 0 poses a problem. In the range ζ ∈ [0, 1] it is possible to take the empty anti-De Sitter (aDS) space-time as a reference but it is no longer possible in the range ζ ∈] − ∞, 0[ where the empty space-time is De Sitter and where the energy is not defined beyond the cosmological horizon 11 .…”

Section: Energy and Massmentioning

confidence: 99%

“…The reformulation can have several applications such as, for example, the study of the new degree of freedom G µν and the study of confinement [11]. We will concentrate on the search of solutions to the EYM equations where it appears to be very powerful.…”

Section: Introductionmentioning

confidence: 99%

Einstein - Yang - Mills black hole solutions in three dimensions

Brindejonc

1998

Class. Quantum Grav.

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In this paper, a procedure which gives Euclidean solutions of 3-dimensional Einstein-Yang-Mills equations when one has solutions of the Einstein equations is proposed. The method is based on reformulating Yang-Mills theory in such a way that it becomes a gravity. It is applied to find black hole solutions of the coupled Einstein Yang-Mills equations. 1 Introduction.Solutions of Einstein-Yang-Mills (EYM) equations have already been the motivation for several studies [1]. For most of them the ansatz used is a sophisticated version of the Reissner-Nordstrm solution. This solution teaches a lot about the properties of EYM black holes, but it requires a numerical evaluation in the final stage. Here, a method is proposed to build analytically a family of Euclidean solutions to these equations. In this report, the method is restricted to three dimensions and SU (2) is chosen as the Yang-Mills (YM) group.The study of 3 dimensional gravity is important because it provides a compromise between the triviality of 2-d gravity and the intricacy of the 4-d one. Classically, the Riemann tensor is entirely determined by the Ricci tensor and by the scalar curvature, thus the solutions of the Einstein equations can be studied almost systematically [2]. From the quantum point of view, the formalism proposed by Achùcarro, Townsend, Witten [3,4] shows that 3-d quantum gravity is, in principle, integrable [4] albeit not trivial. It can serve as a good model for exploring the complexity of quantum gravity [5] or at least of quantum field theory in curved space-time.The study of quantum properties by a functional integral means that one has to look for Euclidean solutions that will provide a starting point for a saddle point approximation. This method has shown its efficiency in the development of black hole thermodynamical properties and in quantum cosmology [6]. An important step is to introduce non-trivial matter fields such as the YM field in this procedure.In the present work, the key to finding Euclidean solutions for the EYM equations is based on describing the 3-d YM theory in terms of gauge invariant variables [7]. In this procedure, YM theory takes the form of a gravity. Thus, the EYM equations reduce to those of two coupled gravities. The similarity between the two sets of equations leads to a very simple ansatz which reduces the two coupled equations to one simple Einstein equation.We apply our ansatz to the Euclidean continuation of BTZ black hole which is a particularly interesting three dimensional solution [8] of the Einstein equations. The mass and the energy of the solution are calculated with the help of the quasi-local formalism developed in [9] and [10].

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“…The crucial point here stems from the fact that pure classical Yang-Mills theory hasn't such solutions by reason of scale invariance. In the papers [12,13] it was shown that typical spherically symmetrical solution of pure Yang-Mills theory is an infinite-energy solution with singularity on the finite radius sphere. Therefore, any approaches to finding gluon clusters is based on the various modifications of lagrangians.…”

Section: Introductionmentioning

confidence: 99%