Aspectos Clássicos do MPE não-mínimo - REIS, João Alfíeres Andrade de Simões dos (2021)
The possibility of Lorentz and CPT violation being manifest in nature, has attracted a growing interest on such theories in the recent years. Both theoretical and experimental studies have been carried out addressing the inclusion of Lorentz violating terms into and looking for experimental deviation of the Standard-Model (SM) and General Relativity (GR). This has led to the development of the Standard Model Extension (SME), which is a framework containing modifications that are power-counting renormalizable and consistent with the gauge structure of the SM. More recently, a nonminimal version of the SME was developed for the photon, neutrino, and fermion sector additionally including higher-derivative terms. In this thesis we intend to study the main classical aspects of the nonminimal sectors of the SME. We start with the neutrino sector, where we develop the full propagator of the single-fermion Dirac theory modified by Lorentz violation. Then we study the dispersion equation for a theory of 𝑁 Dirac neutrino and 𝑁 Majorana neutrino flavors, where we employ sophisticated methods of linear algebra to achieve our objetives. Another interesting result concerns the so-called planar electrodynamics. Here, we construct a Lorentz-violating electrodynamics in (1+2) spacetime dimensions from the electromagnetic sector of the nonminimal Standard-Model Extension (SME) in (1+3) dimensions. From the theory, we study the basic properties such as: field equations, the Green’s functions, the perturbative Feynman rules, and, finally, the modified dispersion relations of the electromagnetic field. Finally, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal Standard-Model Extension (SME). We also derive classical Lagrangians for the operators ^𝑏𝜇 and 𝐻^ 𝜇𝜈 as perturbative expansions in Lorentz violation. Such Lagrangian are of fundamental importance for the description of a relativistic point particle.