A model for Hopfions on the space–time S3×R

Carli, Eduardo De; Ferreira, L. A.

doi:10.1063/1.1829911

Cited by 22 publications

(37 citation statements)

References 14 publications

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“…Our work complements that of ref. [5] where time dependent solitons for the same model were also constructed. In addition, our solutions present properties similar to those of the solitons constructed in [6] for a theory with the same Lagrangean but on Minkowski space-time.…”

Section: Jhep03(2006)097mentioning

confidence: 99%

Annealing Effects on Ge/SiO₂ Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Yoshitake

Kikkawa

Nakamura

et al. 2011

Jpn. J. Appl. Phys.

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We consider a field theory with target space being the two dimensional sphere S 2 and defined on the space-time S 3 × R. The Lagrangean is the square of the pullback of the area form on S 2 . It is invariant under the conformal group SO(4, 2) and the infinite dimensional group of area preserving diffeomorphisms of S 2 . We construct an infinite number of exact soliton solutions with non-trivial Hopf topological charges. The solutions spin with a frequency which is bounded above by a quantity proportional to the inverse of the radius of S 3 . The construction of the solutions is made possible by an ansatz which explores the conformal symmetry and a U (1) subgroup of the area preserving diffeomorphism group.

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Section: Jhep03(2006)097mentioning

confidence: 99%

Annealing Effects on Ge/SiO₂ Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Yoshitake

Kikkawa

Nakamura

et al. 2011

Jpn. J. Appl. Phys.

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“…For instance, static soliton solutions have been found in [28] for the Lagrangian L 4 and the three-sphere S 3 as base space (that is, space-time S 3 × IR). These static solutions solve the Euler-Lagrange equations which follow from varying the static energy functional…”

Section: Discussionmentioning

confidence: 99%

Soliton stability in some knot soliton models

Adam

Sánchez-Guillén

Wereszczyński

2007

Journal of Mathematical Physics

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We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charge (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not even critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.

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“…A similar solution exists in a special critical case in an extended Skyrme-Faddeev model considered in [24]. It would be interesting to study possible physical implications of such models especially in description of monopoles.…”

Section: Fig 2: Energy Density Plots With Afz Ansatz For Hopf Chargementioning

confidence: 98%

Exact knot solutions in a generalized Skyrme-Faddeev model

2013

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We propose a generalized Skyrme-Faddeev type theory with an additional scalar field. In a special case of model parameters one has a theory which admits exact knot solutions given by a class of exact toroidal solitons from Aratyn-Ferreira-Zimerman (AFZ) integrable CP 1 model. In a general case the theory admits an exact knot solution for a unit Hopf charge. For higher Hopf charges we perform numeric analysis of the solutions and obtain estimates for the knot energies using energy minimization procedure based on ansatz with AFZ field configurations and with rational functions. We show that AFZ configurations provide a better approximate solutions. The corresponding knot energies are in a good agreement with a standard law for the low energy bound, EH Q [6,7]. The Skyrme-Faddeev theory [8,9] represents another kind of effective theories which supposed to be induced from quantum chromodynamics (QCD) in low energy regime. The theory possesses topological knot solitons classified by the homotopy group π 3 (CP 1 ) = Z, i.e., by the topological Hopf charge. It is proposed to interpret such knot solutions as color electric and color magnetic glueball states [8,[10][11][12][13]. One should notice, that derivation of a strict expression for a low energy effective action from the basics of QCD is an extremely difficult problem [14][15][16]. So far there exists a number of various extended Skyrme-Faddeev models where some exact and numeric knot and vortex solutions have been found [17][18][19][20].In the present paper we consider an extended SkyrmeFaddeev model with an additional scalar field. In general the low energy effective action of QCD contains scalar fields [10] which originate from unknown coefficient correlation functions in the effective action and play roles of order parameters in the effective theory [14]. We consider a minimal extension of the Skyrme-Faddeev theory to find out a model which is similar to the Skyrme theory, and, at the same time, inherits properties of integrable CP 1 models.So far, all known topological solutions in (3+1) Skyrme type models are obtained numerically except the original Skyrmion soliton [1]. Some exact vortex solutions have been obtained in a generalized Skyrme-Faddeev theory for a special set of model parameters which imply the existence of integrable submodel in the theory [17][18][19]. A family of exact analytic knot solutions with toroidal configuration have been constructed in special integrable CP 1 models [21,22]. Unfortunately, physical applications of such solutions in QCD remain unclear. We propose a Skyrme-Faddeev-type model which admits exact knot solutions and which can give some hints towards constructing a more realistic low energy QCD effective theory. Let us consider an extended Skyrme-Faddeev model defined by the following Lagrangianwheren is a unit triplet field in adjoint representation of SU (2) color group, i.e., CP 1 field, φ is a real scalar field, and H µν is a magnetic field defined as followsµ, β, ν, ξ are model parameters. The first two terms in (1) ...

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A model for Hopfions on the space–time S3×R

Cited by 22 publications

References 14 publications

Annealing Effects on Ge/SiO₂ Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Annealing Effects on Ge/SiO₂ Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Soliton stability in some knot soliton models

Exact knot solutions in a generalized Skyrme-Faddeev model

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A model for Hopfions on the space–time S3×R

Cited by 22 publications

References 14 publications

Annealing Effects on Ge/SiO2 Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Annealing Effects on Ge/SiO2 Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Soliton stability in some knot soliton models

Exact knot solutions in a generalized Skyrme-Faddeev model

Contact Info

Product

Resources

About

Annealing Effects on Ge/SiO₂ Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates

Annealing Effects on Ge/SiO₂ Interface Structure in Wafer-Bonded Germanium-on-Insulator Substrates