Geometry of multisymplectic Hamiltonian first-order field theories

Echeverría-Enríquez, A.; Muñoz-Lecanda, Miguel C.; Román‐Roy, Narciso

doi:10.1063/1.1308075

Cited by 72 publications

(122 citation statements)

References 39 publications

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“…The construction of the Hamiltonian formalism in J 1 π * was pionered in [6] (see also [11] and [12]), while a formulation in Mπ has been stated recently [41]. In the following sections we review the main concepts of the formalism in J 1 π * , and we make an extensive development of the formalism in Mπ.…”

Section: Multimomentum Bundlesmentioning

confidence: 99%

“…Furthermore, if J 1 π → E → M denotes the first-order jet bundle over E, the set made of the affine maps from J 1 π to Λ m T * M , denoted as Aff(J 1 π, Λ m T * M ), is another bundle over E which is canonically diffeomorphic to Λ m 2 T * E [6], [12]. We will denote…”

Section: Multimomentum Bundlesmentioning

confidence: 99%

“…In order to write a set of covariant Hamiltonian equations we must use a global Hamiltonian function, that is, a Hamiltonian density (see [6] and [12] for comments on this subject).…”

Section: Variational Principle and Field Equationsmentioning

confidence: 99%

“…First, several Hamiltonian models can be stated, and the equivalence among them is not always clear (see, for instance, [2], [12], [19], [21], [22], [23], [40], [43]). Furthermore, there are equivalent Lagrangian models with non-equivalent Hamiltonian descriptions [26], [27], [28].…”

Section: Introductionmentioning

confidence: 99%

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Extended Hamiltonian systems in multisymplectic field theories

Echeverría-Enríquez¹,

León

Muñoz-Lecanda³

et al. 2007

Journal of Mathematical Physics

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We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the Hamiltonian field equations. In an analogous way to how these systems are defined in the so-called extended (symplectic) formulation of non-autonomous mechanics, we introduce Hamiltonian systems in the extended multimomentum bundle. The geometric properties of these systems are studied, the Hamiltonian equations are analyzed using integrable multivector fields, the corresponding variational principle is also stated, and the relation between the extended and the restricted Hamiltonian systems is established. All these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.

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Section: Multimomentum Bundlesmentioning

confidence: 99%

Section: Multimomentum Bundlesmentioning

confidence: 99%

“…In order to write a set of covariant Hamiltonian equations we must use a global Hamiltonian function, that is, a Hamiltonian density (see [6] and [12] for comments on this subject).…”

Section: Variational Principle and Field Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extended Hamiltonian systems in multisymplectic field theories

Echeverría-Enríquez¹,

León

Muñoz-Lecanda³

et al. 2007

Journal of Mathematical Physics

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“…Similar constraint algorithms can be developed using equations (4) and (11). Our purpose in the following is to relate these three algorithms.…”

Section: A New Geometric Setting Consider the Fibered Productmentioning

confidence: 99%

A new geometric setting for classical field theories

León

Marrero

Diego

2003

Classical and Quantum Integrability

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Abstract.A new geometrical setting for classical field theories is introduced. This description is strongly inspired by the one due to Skinner and Rusk for singular lagrangian systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.

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Singular Lagrangian Systems on Jet Bundles

et al. 2002

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The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An additional description of constraints is also given considering at the same time compatibility, stability and second order condition problems. Finally, a classification of the constraints in first and second class is obtained using a cosymplectic geometry setting. Using the second class constraints, a Dirac bracket is introduced, extending the well-known construction by Dirac.

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Geometry of multisymplectic Hamiltonian first-order field theories

Cited by 72 publications

References 39 publications

Extended Hamiltonian systems in multisymplectic field theories

Extended Hamiltonian systems in multisymplectic field theories

A new geometric setting for classical field theories

Singular Lagrangian Systems on Jet Bundles

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