The initial chapter of the thesis provides a review of Weinberg’s formalism for the derivation of quantum fields. The formalism is extended to allow for the derivation of quantum fields with more than one spin degree of freedom. It is conjectured that it may be possible to construct massive bosonic quantum field theories of any desired spin j that are consistent and unitary at all energies without the need for regulator terms by including j + 1 spin degrees of freedom: j, j - 1, down to j - j. The concept is then demonstrated in two subsequent chapters by the derivation of a quantum field with spin one and spin zero degrees of freedom followed the derivation of a quantum field with spin two, spin one, and spin zero degrees of freedom. Both field theories are found to be consistent and unitary at all energies without the need for regulator terms. The final two chapters are on unrelated topics. The penultimate chapter provides an explicit derivation of quantum fields for massless particles of spin one-half. In the final chapter, a derivation of the free-space Proca and Maxwell equations is provided via a consistent identification of the linear combinations of the classical fields of the (1,0) and (0,1) representations of the orthochronous Lorentz group.

In both field theories of high energy physics and field theories of condensed matter theories anomalies have been imposing constraints and bringing up new theories. While the perturbational and local anomalies from triangle diagrams are well-developed, we follow and review two works leading to non-perturbational global anomalies both related with Atiyah-Patogi-Sieger (APS) index theorem. In the context of topological fieldtheories the APS index theorem imposes an η-invariant which adds a global anomalous e−iπη/2 to the path integral from each fermions on the boundary. In the case of Pin+ (4) this will require a multiple of 16 Majorana fermions for the global anomaly to cancel. On the other hand with Dai-Freed theorem, global ’t Hooft anomalies concerned to G symmetry group on 4-dimensional spin manifold which is also classifying space BG are studied. The existence of anomalies are related to the triviality of spin bordismgroup Ω Spin5(BG), where examples with SU(2), GSM and Zn are studied with Atiyah-Hirzebruch spectral sequence method and representation of Z n rings. Further there are extensions of spin groups from Pin, SpinZ4 and Spinc , where the anomaly cancellationconstraint of 16 fermions per generation from Spin Z 4 (4) is related to that of Pin + (4) in topological superconductor. A possible candidate of Z4 charge named B − L charge or X charge from several commutative breaking patterns of Spin(10) GUT is briefly discussed with Pati-Salam model and R ⊗ C ⊗ H ⊗ O.

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Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-10T14:58:33Z No. of bitstreams: 1 franciscodelgaudiooliveirafigeuiredo.pdf: 778762 bytes, checksum: 462fd065a0a2a277102c64e0a2ecf79c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T11:51:06Z (GMT) No. of bitstreams: 1 franciscodelgaudiooliveirafigeuiredo.pdf: 778762 bytes, checksum: 462fd065a0a2a277102c64e0a2ecf79c (MD5) / Made available in DSpace on 2018-01-23T11:51:06Z (GMT). No. of bitstreams: 1 franciscodelgaudiooliveirafigeuiredo.pdf: 778762 bytes, checksum: 462fd065a0a2a277102c64e0a2ecf79c (MD5) Previous issue date: 2017-03-02 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As exigências de localidade, positividade dos estados e positividade da energia dão origem a comportamentos ruins dos campos quânticos em distâncias pequenas (singularidadesUV). Quando tenta-se construir campos quânticos para partículas de spin s ≥ 1 que satisfazem esse princípios fundamentais, acaba-se ganhando interações não-renormalizaveis. Para spins um e dois, existem campos, no contexto de teorias de calibre, com o mesmo bom comportamento UV que o campo escalar para spin zero. Entretanto, é necessária a introdução de um espaço de estados não-físico, assim como campos não-físicos (ghosts). Motivado por trabalhos anteriores, nós investigamos campos quânticos, para bósons massivos de spin arbitrário, possuindo o mesmo comportamento UV que o campo escalar (s = 0), porém que agem num espaço de Hilbert sem ghosts e são covariantes por transformações de Poincaré. Esses campos, entretanto, não possuem mais localização pontual, estando localizados, ao invés, em semi-retas no espaço de Minkowski que se extendem em direções tipo-luz (strings tipo-luz). / The combined requirements of locality, positivity of states and positivity of energy lead to bad short distance behaviour of quantum fields (UV singularities). When one tries to build quantum fields for particles of spin s ≥ 1 that still satisfy these fundamental principles, one ends up with non-renormalizable interactions. For spin one and two, there exist fields in the context of gauge theory with the same good UV behaviour as the scalar field for spin zero. However, for this one has to introduce an unphysical state space, as well as unphysical fields (ghosts). Motivated by previous works, we begin to investigate quantum fields, for massive bosons of any spin, that have the same good UV behaviour as the scalar field (s = 0), act in a Hilbert space without ghosts and are Poincaré covariant. These fields are, however, no longer point-local, being localized instead on semi-infinite lines in Minkowski space extending to lightlike infinity (lightlike strings).

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-08T13:15:08Z No. of bitstreams: 1 dantedonizetipereira.pdf: 460175 bytes, checksum: 092f58c5d71aa77ff03d0ae0604294a1 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-26T18:10:56Z (GMT) No. of bitstreams: 1 dantedonizetipereira.pdf: 460175 bytes, checksum: 092f58c5d71aa77ff03d0ae0604294a1 (MD5) / Made available in DSpace on 2017-06-26T18:10:56Z (GMT). No. of bitstreams: 1 dantedonizetipereira.pdf: 460175 bytes, checksum: 092f58c5d71aa77ff03d0ae0604294a1 (MD5) Previous issue date: 2013-07-18 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese exploramos diferentes aspectos de teorias clássicas e quânticas de campos. Na parte clássica, examinamos o fenômeno da birrefringência eletro-magneto-óptica em ele-trodinâmica não-linear no contexto de meios materiais dielétricos não-lineares como uma correção efetiva à teoria linear maxwelliana do eletromagnetismo. Na parte quântica, seguindo o método do heat kernel em teoria quântica de campos sobre espaços curvos, derivamos e estudamos a estrutura das divergências a 1-loop para a ação efetiva de diferentes modelos. Em particular, no ramo do modelo de Yukawa, exibimos duas novas formas de ambiguidades as quais tomam lugar na ação efetiva de campos fermiônicos através do fenômeno da anomalia multiplicativa não-local. Além disso, analisamos a estrutura das divergências ultravioletas a 1-loop para um modelo recentemente proposto de gravitação massiva livre de fantasmas, e mostramos que esse modelo encontra sérias dificuldades no nível quântico. / In this thesis we explore different aspects in classical and quantum field theories. In the classical part, we examine the phenomenon of electro-magneto-optical birefringence in nonlinear electrodynamics in the context of nonlinear dielectric media as an effective correction to the linear Maxwellian theory of electromagnetism. In the quantum part, following the heat kernel method in quantum field theory on curved spaces, we derive and study the structure of the 1-loop divergences for the effective action of different models. In particular, through the Yukawa model, we show two new forms of ambiguities which take place in the effective action of fermionic fields through the phenomenon of nonlocal multiplicative anomaly. Moreover, we analyzed the structure of ultraviolet divergences at 1-loop for a recently proposed ghost-free massive gravity model, and we show that this model meets serious difficulties at the quantum level.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-08-18T17:45:24Z No. of bitstreams: 1 lucastavarescardoso.pdf: 837625 bytes, checksum: 3abd29cb3035fdd6ec6e11d4ea0ae1ae (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-24T12:02:18Z (GMT) No. of bitstreams: 1 lucastavarescardoso.pdf: 837625 bytes, checksum: 3abd29cb3035fdd6ec6e11d4ea0ae1ae (MD5) / Made available in DSpace on 2017-08-24T12:02:18Z (GMT). No. of bitstreams: 1 lucastavarescardoso.pdf: 837625 bytes, checksum: 3abd29cb3035fdd6ec6e11d4ea0ae1ae (MD5) Previous issue date: 2017-08-03 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A construção de campos com localização em cordas foi realizada rigorosamente há pouco mais de uma década. Nesta abordagem, os campos são operadores em algum espaço de Hilbert, e portanto não há graus de liberdade não-físicos tais como "ghosts". Além de permitir a construção de campos carregados inteiramente num espaço espaço de Hilbert, os campos com localização em cordas exibem um bom comportamento no regime ultravioleta e, entre outras características, são possíveis candidatos para descreverem consistentemente a matéria escura. No intuito de obter uma prova da renormalizabilidade em modelos perturbativos no esquema de Epstein-Glaser com campos quânticos localizados em cordas, é necessário evidenciar a liberdade que se tem ao definir produtos temporalmente ordenados do Lagrangeano de interação. Este trabalho proporciona um primeiro passo significativo nesta direção. O problema básico é a presença de um conjunto aberto de n-uplas de cordas que não podem ser cronologicamente ordenadas. Nós resolvemos este problema ao mostrar que quase todas (i.e. exceto num subconjunto de medida nula) tais configurações de cordas podem ser dissecadas num número finito de pedaços, os quais por sua vez podem ser cronologicamente ordenados. Com isso, tem-se que o produto temporalmente ordenado de fatores lineares de campos está fixo fora de um conjunto de medida nula de configurações de cordas. A construção do ordenamento temporal geométrico de cordas é feita de modo a servir para o estudo da renormalizabilidade de quaisquer teorias quânticas de campos com localização em cordas. / The construction of string-localized fields was rigorously accomplished a little over a decade ago. In this approach, the fields are operators in some Hilbert space, and therefore there are no unphysical degrees of freedom such as ghosts. In addition to allowing the construction of charged fields entirely in a Hilbert space, the string-localized fields exhibit, in general, a good behavior in the ultraviolet regime and, among other features, the class (representation) of string-localized fields with m = 0 and s = oo are possible candidates to consistently describe dark matter. In order to obtain a proof of renormalizability of perturbative models in the Epstein—Glaser scheme with string-localized quantum fields, one needs to know what freedom one has to define time-ordered products of the interaction Lagrangian. This work provides a first significant step in that direction. The basic issue is the presence of an open set of n-tuples of strings which cannot be chronologically ordered. We resolve it by showing that almost all (i.e. outside a null set) such string configurations can be dissected into finitely many pieces which can indeed be chronologically ordered. This fixes the time-ordered products of linear field factors outside a nullset of string configurations. The construction of the geometric time ordering of strings is realized in such a way that it will serve to study the renormalizability of any quantum field theories with string-localized fields