In the jet bundle description of field theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for this formalism can be stated, and, on each one of them, the differentiable structures needed for setting the formalism are obtained in different ways. In this work we make an accurate study of some of these Hamiltonian formalisms, showing their equivalence. In particular, the geometrical structures (canonical or not) needed for the Hamiltonian formalism, are introduced and compared, and the derivation of Hamiltonian field equations from the corresponding variational principle is shown in detail. Furthermore, the Hamiltonian formalism of systems described by Lagrangians is performed, both for the hyper-regular and almost-regular cases. Finally, the role of connections in the construction of Hamiltonian field theories is clarified.
Skip Nav Destination
Article navigation
November 2000
Research Article|
November 01 2000
Geometry of multisymplectic Hamiltonian first-order field theories
Arturo Echeverria-Enrı́quez;
Arturo Echeverria-Enrı́quez
Departamento de Matemática Aplicada y Telemática, Edificio C-3, Campus Norte UPC, C/Jordi Girona 1, E-08034 Barcelona, Spain
Search for other works by this author on:
Miguel C. Muñoz-Lecanda;
Miguel C. Muñoz-Lecanda
Departamento de Matemática Aplicada y Telemática, Edificio C-3, Campus Norte UPC, C/Jordi Girona 1, E-08034 Barcelona, Spain
Search for other works by this author on:
Narciso Román-Roy
Narciso Román-Roy
Departamento de Matemática Aplicada y Telemática, Edificio C-3, Campus Norte UPC, C/Jordi Girona 1, E-08034 Barcelona, Spain
Search for other works by this author on:
J. Math. Phys. 41, 7402–7444 (2000)
Article history
Received:
April 21 2000
Accepted:
June 08 2000
Citation
Arturo Echeverria-Enrı́quez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy; Geometry of multisymplectic Hamiltonian first-order field theories. J. Math. Phys. 1 November 2000; 41 (11): 7402–7444. https://doi.org/10.1063/1.1308075
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Related Content
Extended Hamiltonian systems in multisymplectic field theories
J. Math. Phys. (November 2007)
Hamiltonian multivector fields and Poisson forms in multisymplectic field theory
J. Math. Phys. (November 2005)
Lagrangian–Hamiltonian unified formalism for field theory
J. Math. Phys. (January 2004)
On variations in discrete mechanics and field theory
J. Math. Phys. (December 2003)
Constructing a class of solutions for the Hamilton-Jacobi equation in field theory
J. Math. Phys. (November 2007)