Aspectos não perturbativos das teorias de Yang-Mills.

• Autor(a) principal: Sobreiro, Rodrigo Ferreira
• Data de Publicação: 2007
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/12830
• topic: Yang-Mills theories; Quantum chromodynamics; Confinement; Dynamical mass generation; Gluons; Condensates; Teorias de Yang-Mills; Cromodinâmica quântica (QCD); Confinamento; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA

Some nonperturbative aspects of Euclidean Yang-Mills theories in four dimensions,quantized in the Landau gauge, are analytically studied. In particular, we investigate the dynamical mass generation for the gluons due to the presence of dimension two condensates. This study is performed in the framework of the local composite operator technique in the case of the Yang-Mills action as well as in the case of the Gribov-Zwanziger action. Further, an investigation of the Gribov ambiguities in the linear covariant gauges is presented. In the case of the Yang-Mills action, we perform a detailed analysis of the local composite operator formalism when the operators Aa¹Aa¹ and fabc¹cbcc are simultaneously introduced. Using the algebraic renormalization theory, we prove the renormalizability of the model trough all orders in perturbation theory. With the help of the renormalization group equations, a quantum efective action for the condensates <Aa¹Aa¹> and <fabc¹cbcc> is constructed. This construction is performed by means of the dimensional regularization in the MS renormalization scheme. We show that non vanishing condensates values are dynamically favored, independently of the chosen scale. Explicit one loop computations are then presented, providing estimates for the condensates as well as for the vacuum energy. With the help of suitable Ward identities, we are able to normally show that the presence of the condensate <fabc¹cbcc> is responsible for the breaking of the transversality of the vacuum polarization. However, the gluon propagator remains transverse, trough all orders in perturbation theory. Finally, we end this analysis with the explicit computation of the one loop correction to the efective gluon mass. The result is that, due to the condensate <fabc¹cbcc>, the Abelian and the non Abelian sectors acquire diferent masses. Since the non Abelian mass is larger than the Abelian one, this feature can be interpreted as an evidence for the Abelian dominance principle in the Landau gauge. With respect to the Gribov-Zwanziger action, we start our analysis without taking into account the condensate. We show that, at one loop order, the vacuum energy is always positive, independently of the renormalization scheme and scale. We also present attempts to solve the one and two loops horizon condition in the MS scheme, and also the respective obstacles of it. Later, using the algebraic renormalization theory, we show, to all orders in perturbation theory, the renormalizability of the Gribov-Zwanziger action when the composite operator Aa¹Aa¹ is included in the framework of the local composite operator technique. Attempts to solve the one loop gap equations in the MS scheme are then presented. We show that there are no solutions for <Aa¹Aa¹> < 0 while for <Aa¹Aa¹i> 0 there is only one possible solution for the horizon condition. However, in the MS scheme, we were not able to find explicitly that solution. As an improvement, an optimization of the renormalization scheme is performed in the sense of minimizing the renormalization scheme dependence. In that approach the MS limit solution was found as well as the solution with minimal dependence on the renormalization scheme. In both cases, the vacuum energy shows itself to be positive while the condensate <Aa¹Aa¹> > 0. A discussion of the consequences of a nonvanishing Gribov parameter is then provided. Finally, we present a study of the Gribov ambiguities in the linear covariant gauges for the case α<<1, where α is the gauge parameter. After the identification of a region in field space where there are no close Gribov copies, we perform the respective restriction in the path integral. As a tree level efect, the transverse gluon propagator turns out to be infrared suppressed, due to the presence of the Gribov horizon. The longitudinal component shows itself to be infrared suppressed due to the dynamical mass, associated with the condensate <Aa¹Aa¹>. Further, diferently of the Landau gauge, the ghost propagator is not related to the appearance of long range forces. Instead, an infrared singular Green function related to the Gribov horizon is identifed. This Green function can be associated with long range forces. At the end, all Landau gauge results can be recovered taking the limit α→0.