Dynamical structures fork-vector fields

Martin, Geoffrey

doi:10.1007/bf00668840

Cited by 20 publications

(12 citation statements)

References 4 publications

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“…We add this material for the sake of completeness. It can be found for instance in [3,12]. Usually [10], when considering foliations of a given manifold M, one introduces the notion of distributions, i.e.…”

Section: Appendix a Distributions And Multivectorsmentioning

confidence: 99%

Geometry of Hamiltonian n-vector fields in multisymplectic field theory

Paufler

Römer

2002

Journal of Geometry and Physics

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Multisymplectic geometry-which originates from the well known De Donder-Weyl (DW) theory-is a natural framework for the study of classical field theories. Recently, two algebraic structures have been put forward to encode a given theory algebraically. Those structures are formulated on finite dimensional spaces, which seems to be surprising at first.In this paper, we investigate the correspondence of Hamiltonian functions and certain antisymmetric tensor products of vector fields. The latter turn out to be the proper generalisation of the Hamiltonian vector fields of classical mechanics. Thus we clarify the algebraic description of solutions of the field equations.

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Section: Appendix a Distributions And Multivectorsmentioning

confidence: 99%

Geometry of Hamiltonian n-vector fields in multisymplectic field theory

Paufler

Römer

2002

Journal of Geometry and Physics

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“…An alternative way to derive the field equations is to use the so-called multisymplectic formalism, developed by Tulczyjew's school in Warsaw (see [23,24,25,48]), and independently by García and Pérez-Rendón [11,12] and Goldschmidt and Sternberg [14]. This approach was revised by Martin [35,36] and Gotay et al [15,16,17,18] and more recently by Cantrijn et al [7,8].…”

Section: Introductionmentioning

confidence: 99%

SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

Román‐Roy¹,

Salgado

Vilariño

2007

Rev. Math. Phys.

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This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

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“…The multisymplectic formalism was developed by Tulczyjews school in Warsaw (see, for instance, [17]), and independently by García and Pérez-Rendón [10,11] and Goldschmidt and Sternberg [12]. This approach was revised, among others, by Martin [28,29] and Gotay et al [13] and, more recently, by Cantrijn et al [9].…”

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confidence: 99%

k-symplectic formalism on Lie algebroids

León¹,

Diego²,

Salgado³

et al. 2009

J. Phys. A: Math. Theor.

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In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson sigma models.2000 Mathematics Subject Classification. 53D99, 53Z05, 70S05.

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Dynamical structures fork-vector fields

Cited by 20 publications

References 4 publications

Geometry of Hamiltonian n-vector fields in multisymplectic field theory

Geometry of Hamiltonian n-vector fields in multisymplectic field theory

SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

k-symplectic formalism on Lie algebroids

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