On the degenerate dynamics of branched hamiltonians

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dc.contributor.advisor-co1Zanelli, Jorge
dc.contributor.advisor-co1IDhttps://orcid.org/0000-0001-7512-4284
dc.contributor.advisor1Pinto-Neto, Nelson
dc.contributor.advisor1IDhttps://orcid.org/0000-0001-6713-5290
dc.contributor.authorFerreira Junior, Alexsandre Leite
dc.contributor.referee1Fabris, Júlio
dc.contributor.referee2Piattella, Oliver Fabio
dc.contributor.referee3Bittencourt, Eduardo
dc.contributor.referee4Gannouji, Radouane
dc.contributor.referee5Helayël-Neto, José
dc.date.accessioned2024-11-04T21:47:03Z
dc.date.available2024-11-04T21:47:03Z
dc.date.issued2024-09-21
dc.description.abstractBranched Hamiltonians and the corresponding singularity are present in several inter esting physical systems: Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics. The emergent ill defined sympletic structure and tricky dynamical evolution poses challenges to a consistent interpretation. In this thesis, multi-valued Hamiltonians are investigated in the framework of degenerate dynamical system, whose sympletic form does not have a constant rank, allowing novel features and interpretations not present in previous investigations. In particular, it is shown how the multi-valuedness is associated with a dynamical mechanism of dimensional reduction, as some degrees of freedom turn into gauge symmetries when the system degenerates. In the case of classical time crystal, there is no “moving” ground state nor brick wall solution, as described previously. Moreover, the degenerate dynamics of a k–essence model enables it to be responsible for both primordial inflation and the present observed acceleration of the cosmological background geometry, while also admitting a non-singular de Sitter beginning of the Universe (it arises from de Sitter and ends in de Sitter). Furthermore, the model is free of pathologies such as propagating superluminal perturbations, negative energies, and perturbation instabilities. Henceforth, in thesis is demonstrated that the degenerate dynamics offer a consistent interpretation, under which the degeneracy and consequent branching is not a problem but a dynamical feature.
dc.description.sponsorshipFundação de Amparo à Pesquisa e Inovação do Espírito Santo (FAPES)
dc.formatText
dc.identifier.urihttp://repositorio.ufes.br/handle/10/18121
dc.languagepor
dc.language.isoen_US
dc.publisherUniversidade Federal do Espírito Santo
dc.publisher.countryBR
dc.publisher.courseDoutorado em Astrofísica, Cosmologia e Gravitação
dc.publisher.departmentCentro de Ciências Exatas
dc.publisher.initialsUFES
dc.publisher.programPrograma de Pós-Graduação em Astrofísica, Cosmologia e Gravitação
dc.rightsopen access, restricted access ou embargoed access
dc.subjectNon-linear dynamics
dc.subjectCosmology
dc.subjectBranched hamiltonians
dc.subject.cnpqAstronomia
dc.titleOn the degenerate dynamics of branched hamiltonians
dc.typedoctoralThesis
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Doutorado em Astrofísica, Cosmologia e Gravitação