A descrição dos efeitos da região infravermelha das teorias de Yang-Mills ainda é um problema não resolvido na física teórica. Uma fundamentação que descreva de maneira clara e consistente o fenômeno do confinamento de quárks e glúons está longe de ser obtida. Desta forma, nesta tese estudar-se-á duas diferentes abordagens à quantização das teorias de Yang-Mills que consideram os efeitos das cópias de Gribov. O primeiro cenário é o bem estabelecido modelo de Gribov-Zwanziger reescrito de maneira BRST-invariante, com isso, adicionar-se-á na correspondente ação, campos compostos locais invariantes de calibre tanto bosônicos quanto fermiônicos. Portanto, estender-se-á o modelo para outros calibres que não o de Landau, por exemplo, os calibres lineares covariantes. Assim, realizar-se-á o estudo da prova da renormalizabilidade deste sistema a todas as ordens em teoria de perturbação através do método da renormalização algébrica. O segundo cenário a ser desenvolvido nesta tese foi apresentado na última década, o chamado modelo de Serreau-Tisier, usando este ponto de vista, obter-se-á finalmente uma boa explicação, de primeiros princípios, para a geração da massa do campo de calibre (glúon) presente no modelo particular de Curci-Ferrari através do fenômeno da restauração de simetria. Apresentar-se-á também uma discussão sobre as semelhanças entre o modelo sigma não linear em duas dimensões e a Cromodinâmica Quântica.
The infrared regime of Yang-Mills theories is still an unsolvable problem in theoretical physics. The attempt to describe in a clear and suitable way the phenomenon of confinement of gluons and quarks is far from being finished. In this manuscript, we study two different viewpoints for the quantization of Yang-Mills theories by taking into account the effects of Gribov copies. The first one is the well-known Gribov-Zwanziger framework reinvented by including bosonic and fermionic gauge-invariant local composite fields through a detailed construction of a nonperturbative BRST symmetry. This gives us the possibility to extend this model to another class of gauges in a correct manner, the so-called linear covariant gauges. Then, we prove its renormalizability to all orders in a loop expansion by using the algebraic renormalization method. The Other one is the Serreau-Tissier approach, in this framework we establish a good explanation for the generation of the gauge field (gluon) mass added in the particular Curci-Ferrari phenomenological model proposed by M. Tissier and N. Wschebor by using the symmetry restoration phenomenon. To accomplish that, we also discuss the similarities between the nonlinear sigma models in two space-time dimensions and quantum chromodynamics.
The infrared regime of Yang-Mills theories is still an unsolvable problem in theoretical physics. The attempt to describe in a clear and suitable way the phenomenon of confinement of gluons and quarks is far from being finished. In this manuscript, we study two different viewpoints for the quantization of Yang-Mills theories by taking into account the effects of Gribov copies. The first one is the well-known Gribov-Zwanziger framework reinvented by including bosonic and fermionic gauge-invariant local composite fields through a detailed construction of a nonperturbative BRST symmetry. This gives us the possibility to extend this model to another class of gauges in a correct manner, the so-called linear covariant gauges. Then, we prove its renormalizability to all orders in a loop expansion by using the algebraic renormalization method. The other one is the Serreau-Tissier approach, in this framework we establish a good explanation for the generation of the gauge field (gluon) mass added in the particular Curci-Ferrari phenomenological model proposed by M. Tissier and N. Wschebor by using the symmetry restoration phenomenon. To accomplish that, we also discuss the similarities between the nonlinear sigma models in two space-time dimensions and quantum chromodynamics.
