Erratum: N=4 super KdV hierarchy in N=4 and N=2 superspaces [J. Math. Phys. <b>37</b>, 1356–1381 (1996)]

Delduc, F.; Ivanov, Evgeniy; Krivonos, S.

doi:10.1063/1.531810

Cited by 16 publications

(51 citation statements)

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“…1 It was introduced in [28] (see also [29]) in order to construct an N=4 superextension of the KdV hierarchy, but was never utilized for d=1 sigma model building.…”

Section: Introductionmentioning

confidence: 99%

N= 4 supersymmetric mechanics in harmonic superspace

Ivanov¹,

Lechtenfeld

2003

J. High Energy Phys.

140

384

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We define N =4, d=1 harmonic superspace HR 1+2|4 with an SU(2)/U(1) harmonic part, SU(2) being one of two factors of the R-symmetry group SU(2)× SU(2) of N =4, d=1 Poincaré supersymmetry. We reformulate, in this new setting, the models of N =4 supersymmetric quantum mechanics associated with the off-shell multiplets (3, 4, 1) and (4, 4, 0). The latter admit a natural description as constrained superfields living in an analytic subspace of HR 1+2|4 . We construct the relevant superfield actions consisting of a sigma-model as well as a superpotential parts and demonstrate that the superpotentials can be written off shell in a manifestly N =4 supersymmetric form only in the analytic superspace. The constraints implied by N =4 supersymmetry for the component bosonic target-space metrics, scalar potentials and background one-forms automatically follow from the harmonic superspace description. The analytic superspace is shown to be closed under the most general N =4, d=1 superconformal group D(2, 1; α). We give its action on the analytic superfields comprising the (3, 4, 1) and (4, 4, 0) multiplets, reveal a surprising relation between the latter and present the corresponding superconformally invariant actions. The harmonic superspace approach suggests a natural generalization of these multiplets, with a [2(n+1), 4n, 2(n−1)] off-shell content for n>2.

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“…1 It was introduced in [28] (see also [29]) in order to construct an N=4 superextension of the KdV hierarchy, but was never utilized for d=1 sigma model building.…”

Section: Introductionmentioning

confidence: 99%

N= 4 supersymmetric mechanics in harmonic superspace

Ivanov¹,

Lechtenfeld

2003

J. High Energy Phys.

140

384

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“…The analysis of integrable systems, in particular the Korteweg-de Vries equation and extensions of it [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], have provided a lot of interesting results from both mathematical and physical points of view.…”

Section: Introductionmentioning

confidence: 99%

Singular Lagrangians and Its Corresponding Hamiltonian Structures

Restuccia¹,

Sotomayor²

2017

Lagrangian Mechanics

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We present a general procedure to obtain the Lagrangian and associated Hamiltonian structure for integrable systems of the Helmholtz type. We present the analysis for coupled Korteweg-de Vries systems that are extensions of the Korteweg-de Vries equation. Starting with the system of partial differential equations it is possible to follow the Helmholtz approach to construct one or more Lagrangians whose stationary points coincide with the original system. All the Lagrangians are singular. Following the Dirac approach, we obtain all the constraints of the formulation and construct the Poisson bracket on the physical phase space via the Dirac bracket. We show compatibility of some of these Poisson structures. We obtain the Gardner ε-deformation of these systems and construct a master Lagrangian which describe the coupled systems in the weak ε-limit and its modified version in the strong ε-limit.

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“…Coupled KdV systems were also analyzed in [5][6][7]. An important area of interest of high energy physics related to coupled systems is provided by the supersymmetric extensions of KdV equations [8][9][10][11][12][13][14] and more generally by operator and Cli ord valued extensions of KdV equation [15,16].…”

Section: Introductionmentioning

confidence: 99%

Duality relation among the Hamiltonian structures of a parametric coupled Korteweg-de Vries system

Restuccia

Sotomayor

2016

Open Physics

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Abstract:We obtain the full Hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four di erent real basic lagrangians. The associated Hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated Hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system. We then construct two master lagrangians for the coupled system whose eld equations are the ϵ-parametric Gardner equations obtained from the coupled KdV system through a Gardner transformation. In the weak limit ϵ → the lagrangians reduce to the ones of the coupled KdV system while, after a suitable rede nition of the elds, in the strong limit ϵ → ∞ we obtain the lagrangians of the coupled modi ed KdV system. The Hamiltonian structures of the coupled KdV system follow from the Hamiltonian structures of the master system by taking the two limits ϵ → and ϵ → ∞.

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Erratum: N=4 super KdV hierarchy in N=4 and N=2 superspaces [J. Math. Phys. 37, 1356–1381 (1996)]

Cited by 16 publications

References 0 publications

N= 4 supersymmetric mechanics in harmonic superspace

N= 4 supersymmetric mechanics in harmonic superspace

Singular Lagrangians and Its Corresponding Hamiltonian Structures

Duality relation among the Hamiltonian structures of a parametric coupled Korteweg-de Vries system

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