Quantum effects for extrinsic geometry of strings via the generalized Weierstrass representation

Konopelchenko, B. G.; Landolfi, Giulio

doi:10.1016/s0370-2693(98)01412-9

Cited by 7 publications

(14 citation statements)

References 23 publications

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“…This is a nonlinear elliptic partial differential equation, a natural problem is to solve the Dirichelet problem for the minimal surface equation [11], the problem has a solution for any boundary data if and only if domain is convex.…”

Section: Generalized Weierstrass Representationmentioning

confidence: 99%

“…First of all, we focus our study on the three-dimensional model, the geometry of immersed surfaces in R 3 is reviewed considering Enneper-Weierstrass representation of minimal surfaces. A different approaches has been introduced [11] [7],we show three dimensional Nambu-Goto string and show its equivalent in the minimal surface theory. At this point, a formula of linearized Numbu Goto action depending on Weierstrass parametrization can be established.…”

Section: Introductionmentioning

confidence: 99%

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Nambu-Goto Strings viaWeierstrass Representation

kotb¹

2017

JAP

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A description of string model of gauge theory are related to minimal surfaces. notations of minimal surface and related mean and Gauss curvature discussed. The Weierstrass representation for a surface conformally which immersed in R used to represent Nambu- Goto action, action of Nambu Goto is calculated usingWeierstrass representation which can be used to calculate the Partion Function and potential, then a non-perturbative solution for action is aimed and fulfilled and a consequences of that are investigated and its mathematical and physical properties are discussed.

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Section: Generalized Weierstrass Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nambu-Goto Strings viaWeierstrass Representation

kotb¹

2017

JAP

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“…In particular, to such diverse areas as in the field of two-dimensional gravity [5,6], quantum field theory [5,7], statistical physics [8,9] and fluid dynamics [10,11]. It is worth mentioning an application of recent interest, namely, the propagation of a string through space-time [12]. It describes a surface called its world sheet.…”

Section: )mentioning

confidence: 99%

“…The study of stable classical configurations of strings is one of the most important problems of string theory [6,12]. From a physical point of view, it has been proposed to describe QCD flux tubes, which are responsible for quark confinement using strings, and that QCD strings should take into account the extrinsic geometry of the string world sheet.…”

Section: Application To Classical String Theorymentioning

confidence: 99%

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Symmetry properties and explicit solutions of the generalized Weierstrass system

Bracken

Grundland

2001

Journal of Mathematical Physics

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The method of symmetry reduction is systematically applied to derive several classes of invariant solutions for the generalized Weierstrass system inducing constant mean curvature surfaces and to the associated two-dimensional nonlinear sigma model. A classification of subgroups with generic orbits of codimension one of the Lie point symmetry group for these systems provides a tool for introducing symmetry variables and reduces the initial systems to different nonequivalent systems of ordinary differential equations. We perform a singularity analysis for them in order to establish whether these ordinary differential equations have the Painlevé property. These ordinary differential equations can then be transformed to standard forms and next solved in terms of elementary and Jacobi elliptic functions. This results in a large number of new solutions and in some cases new interesting constant mean curvature surfaces are found. Furthermore, this symmetry analysis is extended to include conditional symmetries by subjecting the original systems to certain differential constraints. In this case, several types of nonsplitting algebraic, trigonometric and hyperbolic multi-soliton solutions have been obtained in explicit form. A new procedure for constructing solutions of the overdetermined system which is composed of the generalized Weierstrass system and the complex eikonal equations is studied. Finally, an approach to the classical configurations of strings in three-dimensional Euclidean space based on the obtained solutions of the generalized Weierstrass system is presented. RésuméLa méthode de réduction par symétries est appliquée systématiquement pour dériver plusieurs classes de solutions invariantes du système de Weierstrass généralisé induisant des surfaces de courbure moyenne constante et du modèle sigma euclidien bidimensionnel associéà ce système. Une classification des sous-groupes avec orbites génériques de codimension un des groupes de Lie de symétrie ponctuels pour ces systèmes fournit un moyen d'introduire des variables de symétrie et réduit le système initialà différents systèmes inéquivalents d'équations différentielles ordinaires. Nous effectuons une analyse des singularités afin d'établir si ceséquations différentielles ordinaires possèdent la propriété de Painlevé. Ceséquations différentielles ordinaires peuvent alorsêtre transformées dans des formes standards et ensuite résolues en termes de fonctionsélémentaires et de fonctions elliptiques de Jacobi. Cela résulte en un grand nombre de nouvelles solutions et, dans certains cas, de nouvelles surfacesà courbure moyenne constante sont trouvées. De plus, cette analyse des symétries estétendue au cas des symétries conditionnelles en soumettant les systèmes initiauxà certaines contraintes différentielles. Dans ce cas, plusieurs solutions multi-solitoniques non-séparantes de type algébrique, trigonomé-trique et elliptique sont obtenues sous une forme explicite. Une nouvelle procédure pour construire des solutions du système surdéterminé composé du ...

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On the Bäcklund transformation and the theorem of permutability for the generalized Weierstrass system

Bracken¹,

Grundland²

2000

Inverse Problems

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The connection between the structure of the second order system describing the Euclidean sigma model equations associated with the generalized Weierstrass system and the possibility of the construction of some classes of solutions is discussed. It is shown using the conditional symmetry method that the Auto-Bäcklund transformation for the generalized Weierstrass system can be constructed. The permutability theorem for this Auto-Bäcklund transformation is formulated. New classes of non-splitting multi-soliton solutions are obtained through the use of the theorem of permutability.

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Quantum effects for extrinsic geometry of strings via the generalized Weierstrass representation

Cited by 7 publications

References 23 publications

Nambu-Goto Strings viaWeierstrass Representation

Nambu-Goto Strings viaWeierstrass Representation

Symmetry properties and explicit solutions of the generalized Weierstrass system

On the Bäcklund transformation and the theorem of permutability for the generalized Weierstrass system

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