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dc.contributor.authorDe León, Manuel
dc.contributor.authorPrieto Martínez, Pedro Daniel
dc.contributor.authorRomán Roy, Narciso
dc.contributor.authorVilariño Fernández, Silvia
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationDe León, M., P.D. Prieto-Martínez, Roman-Roy, N., Vilariño Fernández, S. Hamilton-Jacobi theory in multisymplectic classical field theories. "Journal of mathematical physics", 1 Setembre 2017, vol. 58, p. 2-37.
dc.description.abstractThe geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de Léon et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
dc.format.extent36 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential geometry
dc.subject.lcshField theory (Physics)
dc.titleHamilton-Jacobi theory in multisymplectic classical field theories
dc.subject.lemacGeometria diferencial
dc.subject.lemacCamps, Teoria dels (Física)
dc.contributor.groupUniversitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::53 Differential geometry::53C Global differential geometry
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorDe León, M.; Prieto-Martínez, P.D.; Roman-Roy, N.; Vilariño Fernández, Silvia
local.citation.publicationNameJournal of mathematical physics

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