Potencial efetivo nas teorias tipo Hořava–Lifshitz

Abstract

In the beggining of the 20th century, Quantum Mechanics and Special Relativity changed radically the basic notions of physics. From the merging of the two theories Quantum Field Theory was born, the basis of the Standard Model of Elementary Particles, which describes three of the four fundamental interactions (electromagnetic and the strong and weak forces). The gravitational interaction is described in a very different setting, namelly the classical General Theory of Relativity, whose formulation is quite distinct from the one used for the other interactions. Initial efforts to place the four interactions into the same conceptual framework were unsuccessful. The reason behind it is that, if treated as a quantum field theory, gravity yields divergent results. Several theories were presented as candidates to put gravity at the same footing as other interactions. One of these theories, proposed by Petr Horava in 2009, consists in enhancing the divergence properties of quantum gravity through the introduction of an anisotropic space-time. As Horava’s proposal changes the notions of space and time essentially, one may ask questions about how the usual quantum field theory models behave under such changes. In this thesis we study two quantum field theory models within the context of Horava-like space-time anisotropy. We calculate the effective potential at one loop order for the scalar QED using two methods. The first, Dirac’s method for constrained systems, does not reffer to any type of gauge choice. In the second method we studied the model with a particular choice of gauge fixing, which led to the appearance of Faddeev-Popov ghosts. We have also studied the Gross-Neveu model, for which we calculated the gap equation, showing the dynamical parity breaking and mass generation under specific circumstances. We calculated the gap equation in the finite temperature case, having found the critical temperature for which the parity breaking occurs. We have also analized the renormalization properties of the theory in the 1=N expasion. Finally, we checked for the possibility of generating the Chern-Simons term for this Gross- Neveu model.