Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-27T11:35:41Z No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-07T20:52:19Z (GMT) No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) / Made available in DSpace on 2017-08-07T20:52:19Z (GMT). No. of bitstreams: 1 cleberabrahaodesouza.pdf: 307341 bytes, checksum: f90c47044c5f5aabc5bbb77378b1cd58 (MD5) Previous issue date: 2011-02-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A teoria relativística da gravitação é uma ferramenta fundamental para a compreensão da cosmologia moderna. Ela descreve a dinâmica do campo gravitacional ao longo do espaço-tempo. Dentre os possíveis modelos de universo, um dos mais comuns é o descrito pela métrica de Friedmann-Lemaitre-Robertson-Walker (FLRW). Esta métrica pode ser escrita em termos do tempo conforme e descreve um universo homogêneo e isotrópico. Neste trabalho investigamos os campos de Dirac não massivos neste modelo de universo. Os resultados mostram uma compatibilidade entre as equações de Dirac e a métrica de FLRW. Os efeitos do parâmetro de Immirzi junto com os férmions podem ser descritos em termos de um fluido perfeito usual intermediário entre a poeira e radiação. / The general relativity theory is fundamental tool for understanding the modern cosmology. In this work we investigated the massless Dirac fields in the Friedamm-Lamaitre-Robertson-Walker universe. The metric is written in terms of conformal time which describes a homogeneous and isotropic universe. We show that the effects of Immirzi parameter along with the fermions can be described in terms of a usual perfect fluid intermediate between dust and radiation.

The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula. Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed. It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.

The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula. Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed. It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.