Espalhamento eletron-múon na eletrodinâmica quântica com temperatura finita

Abstract

This work aims to evaluate the cross section for the electron-muon scattering process in Quantum Electrodynamics at finite temperature. We’ll initially introduced the basic properties of canonical quantization and discuss the interaction formalism to λφ4, Yukawa and QED theory. The Feynman’s rules to the scattering matrix M and therefore to the cross section are first evaluated at zero temperature. On the second part of this work the thermal effects are to be considered through Thermo Field Dynamics (TFD) formalism. This has as its main feature the constructionofathermalvacuumstatebydoublingthedegreesoffreedomofthesystemwhich in turn generates a duplicate Hilbert space called a thermal Hilbert space. As an immediate consequence, it will be possible to construct a operator U(β), called Bogoliubov transformation operator, which will allow to introduce thermal operators so that the techniques developed at zero temperature can be easily generalized for the finite temperature case. In fact,the thermal propagators for the scalar and Dirac fields will be evaluated without much difficulty through a procedure quite analogous to the conventional Quantum Field Theory (QFT) procedure. The thermal photon propagator will also be calculated, but by a quite different procedure. As we will see, it will be possible to define a matrix product that will lead to a propagating matrix whose elements of the main diagonal are, respectively, the thermal propagators of the photon in the original and tilde space. Feynman’s rules for the temperature-dependent scattering matrix M(β) are also evaluated. In view of the doubling freedom degrees of the system, the DCT formalism will introduce new interaction vertices to take into account the tilde system, so that the number of Feynman diagrams contributing to the scattering will be doubled. Finally, the temperature-modified cross section is explicitly calculated and, through limit analysis, it will be concluded that as the temperature increases, the particles involved spread less and less to a certain limit value of the cross section.