Espalhamento compton gravitacional à temperatura finita

Abstract

In this work, we will explore the fundamental concepts of Gravitoelectromagnetic Theory (GEM), presenting its main mathematical framework, as well as its physical concepts and interpretations. As an example, we will apply the GEM theory to a physical scenario. From this application, we derive the GEM energy-momentum tensor, a fundamental physical quantity that is directly related to the conservation of energy and momentum. Furthermore, we will investigate gravitational Compton scattering, which involves an interaction between a fermion and a graviton, with an antifermion acting as the intermediate particle. To conduct a more comprehensive study of this process, it is essential to determine two key parameters in particle physics: the transition amplitude and the cross-section. The transition amplitude indicates the probability of a specific interaction occurring within a system, while the cross-section describes how this probability is distributed in a specific region of space. With these two parameters, we achieve a complete description of the interaction between particles and their energy and momentum transfers. As a result, we have that the GEM cross section differs from Quantum Electrodynamics both in structure and coupling constants. Additionally, we will discuss how this process behaves when considering thermal effects in the system. To introduce thermal effects, we will use the Thermo Field Dynamics (TFD) formalism. TFD is a framework within quantum field theory that allows us to incorporate temperature into systems in thermal equilibrium. To do so, it is necessary to duplicate the usual Hilbert space and apply Bogoliubov transformations, which facilitate the definition of a thermal vacuum state and the corresponding thermal creation and annihilation operators. When applied to scattering, we observe that in the zero temperature regime, we recover the case at zero temperature, while, for high temperatures, the thermal function dominates, this being the predominant factor in the process.