Infrared Effects in QCD at finite temperature

Abstract

Conceive a renormalizable quantum theory of gravitation and understand the phase transition associated with confinement are two of the greatest challenges in modern physics. The basic objective of this research project aims to obtain some results, which may be useful for a better understanding of certain aspects involved in these problems.A fundamental theory of gravitation could eventually be a string theory. However,certain difficulties still remain in implementing this idea. In this way, it was useful to considera simpler alternative proposal that could clarify certain aspects of non-renormalizability. Our proposal was based on the Lagrange multiplier field method, which has the potentialability to eliminate ultraviolet divergences in Feynman multi-loops. In view of the complexity of quantum gravity, we intend to initially apply this method to the Yang-Mills theory in 6 dimensions. This theory, which is non-renormalizable, can be considered as a more accurate model. Posteriorly, we apply this method to quantum gravity described by the Einstein-Hilbert action. Then, for future execution, we will consider the infrared behavior problem of QCD at finite temperature. As we explained in the project, in QCD at zero temperature, in contrast to what happens in QED, infrared divergences do not cancel at the level of two Feynmann loops, due to the non-abelian properties of this theory. This infrared behavior reflects the long-distance confining character of QCD at zero temperature. One of the objectives of this project are to generalize this result to QCD in the high temperature regime.The infrared behavior in this regime may reflect, in a way, the phase transition that occurs in QCD in the high temperature region. (AU)