Modelos generalizados de Chern-Pontryagin e uma nova teoria de espinores não-locais

Abstract

This thesis discusses modified theories of gravitation, exploring aspects inherent to causality, unitarity, renormalizability, Lorentz invariance and CPT symmetry breaking, with emphasis on the original results extracted from two new categories of models: i) generalized Chern- Pontryagin gravity models; and ii) the non-local spin-1/2 field model, in Minkowski space. In the first case, we formulate a new class of modified gravity models in 4 dimensions, whose action is characterized by an arbitrary function of the Ricci scalar and the topological Chern-Pontryagin term ∗RR. Within this framework, we derive the gravitational field equations and solve them for a particular model fI (R, ∗RR) = R+β(∗RR)2 and fII(R, ∗RR) = R + αR2 + β(∗RR)2, considering two ansatzes: the slowly rotating Schwarzschild metric and first-order perturbations of Gödel-type metrics. For the former, considering slowly rotating Schwarzschild metric, we find a first-order correction to the frame dragging effect boosted by the parameter L, which characterizes the departures from general relativity results. We show that generalized four-dimensional Chern-Pontryagin models admit a scalar-tensor representation, whose explicit form presents two scalar fields: Φ, a dynamical degree of freedom (scalaron). In contrast, the second, ϕ, is a non-dynamical degree of freedom, which arises coupled with the Chern-Pontryagin topological term ∗RR, that is, ϕ ∗RR, which is nothing more than the gravitational Chern-Simons term. In the latter model, we create a novel nonlocal spin-1/2 field theory in which the form factors depend on the Dirac operator rather than on the d’Alembert operator. At the classical level, we investigate the dispersion relation of free spin-1/2 particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-1/2 theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit. At the same time, in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale Λ. We minimally couple a U(1) gauge field to the non-local spin-1/2 field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality on the gs-factor of massive particles.