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Reduction of polysymplectic manifolds

dc.contributor.authorMarrero, Juan Carlos
dc.contributor.authorRomán Roy, Narciso
dc.contributor.authorSalgado Seco, Modesto
dc.contributor.authorVilariño, Silvia
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2015-09-23T13:01:38Z
dc.date.available2015-09-23T13:01:38Z
dc.date.created2015-02-06
dc.date.issued2015-02-06
dc.identifier.citationMarrero, J., Roman-Roy, N., Salgado, M., Vilariño, S. Reduction of polysymplectic manifolds. "Journal of physics A. Mathematical and theoretical", 06 Febrer 2015, núm. 5, p. 1-33.
dc.identifier.issn1751-8113
dc.identifier.urihttp://hdl.handle.net/2117/77056
dc.description.abstractThe aim of this paper is to generalize the classical Marsden-Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems with symmetries, such as those appearing in certain kinds of classical field theories. As an application of this technique, an analogue to the Kirillov-Kostant- Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in previous papers (Gunther 1987 J. Differ. Geom. 25 23-53; Munteanu et al 2004 J. Math. Phys. 45 1730-51) on this subject.
dc.format.extent33 p.
dc.language.isoeng
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subject.lcshHamiltonian systems
dc.subject.otherpolysymplectic manifolds
dc.subject.otherMarsden-Weinstein reduction
dc.subject.otherk-coadjoint orbits
dc.subject.otherpolysymplectic Hamiltonian systems
dc.subject.otherNONHOLONOMIC MECHANICAL SYSTEMS
dc.subject.otherCLASSICAL FIELD-THEORY
dc.subject.otherMULTI-MOMENT MAPS
dc.subject.otherSYMMETRIES
dc.subject.otherFORMALISM
dc.subject.otherDYNAMICS
dc.subject.otherSPACES
dc.titleReduction of polysymplectic manifolds
dc.typeArticle
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
dc.identifier.doi10.1088/1751-8113/48/5/055206
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.relation.publisherversionhttp://arxiv.org/abs/1306.0337
dc.rights.accessOpen Access
local.identifier.drac15432686
dc.description.versionPostprint (author’s final draft)
local.citation.authorMarrero, J.; Roman-Roy, N.; Salgado, M.; Vilariño, S.
local.citation.publicationNameJournal of physics A. Mathematical and theoretical
local.citation.volume48
local.citation.number5
local.citation.startingPage1
local.citation.endingPage33


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