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dc.contributor.authorMir Garcia, Pau
dc.contributor.authorMiranda Galcerán, Eva
dc.contributor.otherUniversitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2021-07-01T12:48:49Z
dc.date.available2021-07-01T12:48:49Z
dc.date.issued2021-09
dc.identifier.citationMir, P.; Miranda, E. Geometric quantization via cotangent models. "Analysis and Mathematical Physics", Setembre 2021, vol. 11, núm. 3, p. art-118.
dc.identifier.issn1664-2368
dc.identifier.urihttp://hdl.handle.net/2117/348245
dc.description.abstractIn this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the cotangent models in [13] by both considering singular orbits and adding to the cotangent models a model for the prequantum line bundle. These singularities are generic in the sense that are given by Morse-type functions and include elliptic, hyperbolic and focus-focus singularities. Examples of systems admitting such singularities are toric, semitoric and almost toric manifolds, as well as physical systems such as the coupling of harmonic oscillators, the spherical pendulum or the reduction of the Euler’s equations of the rigid body on T *(SO(3)) to a sphere. Our geometric quantization formulation coincides with the models given in [11] and [21] away from the singularities and corrects former models for hyperbolic and focus-focus singularities cancelling out the infinite dimensional contributions obtained by former approaches. The geometric quantization models provided here match the classical physical methods for mechanical systems such as the spherical pendulum as presented in [4]. Our cotangent models obey a local-to-global principle and can be glued to determine the geometric quantization of the global systems even if the global symplectic classification of the systems is not known in general.
dc.language.isoeng
dc.rightsAttribution 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshGeometric quantization
dc.subject.lcshSingularities (Mathematics)
dc.subject.otherGeometric quantization
dc.subject.otherSymplectic geometry
dc.subject.otherReal polarization
dc.subject.otherSingularities
dc.subject.otherCotangent models
dc.titleGeometric quantization via cotangent models
dc.typeArticle
dc.subject.lemacQuantització geomètrica
dc.subject.lemacSingularitats (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.identifier.doi10.1007/s13324-021-00559-4
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.springer.com/journal/13324
dc.rights.accessOpen Access
local.identifier.drac31862713
dc.description.versionPostprint (published version)
local.citation.authorMir, P.; Miranda, E.
local.citation.publicationNameAnalysis and Mathematical Physics
local.citation.volume11
local.citation.number3
local.citation.startingPageart
local.citation.endingPage118


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