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Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Modelización, Simulación Numérica y Matemática Industriales
dc.contributor.authorBarbero G., J. Fernando
dc.contributor.authorBasquens, Marc
dc.contributor.authorDíaz Jiménez, Bogar
dc.contributor.authorSánchez Villaseñor, Eduardo Jesús
dc.contributor.funderComunidad de Madrides
dc.contributor.funderEuropean Commissionen
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.contributor.funderUniversidad Carlos III de Madrides
dc.date.accessioned2022-11-29T08:36:10Z
dc.date.available2023-10-31T00:00:06Z
dc.date.issued2022-10-31
dc.description.abstractThe purpose of this paper is to discuss a number of issues that crop up in the computation of Poisson brackets in field theories. This is specially important for the canonical approaches to quantization and, in particular, for loop quantum gravity. We illustrate the main points by working out several examples. Due attention is paid to relevant analytic issues that are unavoidable in order to properly understand how computations should be carried out. Although the functional spaces that we use throughout the paper will likely have to be modified in order to deal with specific physical theories such as general relativity, many of the points that we will raise will also be relevant in that context. The specific example of the mock holonomy-flux algebra will be considered in some detail and used to draw some conclusions regarding the loop quantum gravity formalism.en
dc.description.sponsorshipThis work has been supported by the grant PID2020-116567GB-C22 funded byMCIN/AEI/10.13039/ 501100011033. E J S Villaseñor is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors(EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). Bogar Díaz acknowledges support from the CONEX-Plus programme funded by Universidad Carlos III de Madrid and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 801538.en
dc.format.extent22
dc.identifier.bibliographicCitationFernando Barbero G, J., Basquens, M., Díaz, B. & Villaseñor, E. J. S. (2022). Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra. Physica Scripta, 97(12), 125202.en
dc.identifier.doi10.1088/1402-4896/ac99a9
dc.identifier.issn0031-8949
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue12
dc.identifier.publicationlastpage22
dc.identifier.publicationtitlePhysica Scriptaen
dc.identifier.publicationvolume97
dc.identifier.urihttp://hdl.handle.net/10016/36119
dc.identifier.uxxiAR/0000031337
dc.language.isoeng
dc.publisherIOP Publisingen
dc.relation.projectIDGobierno de España. PID2020-116567GB-C22es
dc.relation.projectIDComunidad de Madrid. EPUC3M23es
dc.relation.projectIDUniversidad Carlos III de Madrid. CONEX-Plus programmees
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/801538en
dc.rights© 2022 IOP Publishing Ltden
dc.rights.accessRightsopen accessen
dc.subject.ecienciaFísicaes
dc.subject.ecienciaMatemáticases
dc.subject.otherPoisson bracketsen
dc.subject.otherHolonomy-flux algebraen
dc.subject.otherLoop quantum gravityen
dc.subject.otherSobolev spacesen
dc.titlePoisson brackets in Sobolev spaces: a mock holonomy-flux algebraen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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