Eletrodinâmicas do MPE não-mínimo com altas derivadas e violação da simetria de Lorentz.

Abstract

In this thesis, we present a review of Podolsky’s and Maxwell’s electrodynamics modified by a higher-derivative, CPT-even and dimension-6 term. For Podolsky’s electrodynamics we analyze the equations of motion and find the solution for the electrostatic potential through Green’s method. We also calculate the Feynman propagator and, by combining the poles, we get the dispersion relations of the theory, which allows us to evaluate causality, stability and unitarity of the theory. We study a generalization of Maxwell’s electrodynamics involving anisotropic, CPT-even, Podolsky and Lee-Wick terms. Furthermore, we examine a CPT-odd, higher-derivative and dimension-5 electrodynamics of the nonminimal Standard-Model Extension (SME) coupled to a tensor that controls Lo rentz violation. The modification introduced has the form: κλµνDκAλ Fµν. We calculate the propagator of the theory and we also analyze the dispersion relations for the isotropic and anisotropic sectors. We verified that causality is valid for all parameters that we choose; howe ver unitarity of the theory is not guaranteed. Analogously, we study the dimension-5 term, given by κλµνAλTκ(T · ∂) 2Fµν with higher derivatives, which is directly linked to the theory of Myers-Pospelov for photons. In this model we obtain, for a time-like tensor background, two propagation modes. One of them is causal, while the other one isn’t. Unitarity is preserved while energy remains real, even for the noncausal mode. For the spacelike background, causality is violated within certain regimes. However, there are particular configurations that preserve unitarity and there are strong numerical indications that unitarity is guaranteed for all purely spacelike configurations. We also examine the term κλµνDκAλ Fµν. In this context, we analyze the classical aspects of the modified Maxwell equations and calculate the four-potential Aµ in order to obtain the electric and magnetic fields modified by the Lorentz-violating tensor. Finally, we investigate a modified planar electrodynamics. We propose a Chern-Simons like theory in (1 + 2) dimensions endowed with higher derivatives and Lorentz violation. The electromagnetic sector has a CPT-odd contribution, ε λµνAλ( ˆkAF )Fµν, which is related to a generalized Chern-Simons-like term.