Symmetrical groups and quantum field theory

Abstract

This Scientific Initiation Project proposes to develop a study program focused on theoretical research of many topics related to Quantum Field Theory. In particular, the role of symmetries on the development of the Standart Model of particle physics. Starting with Lie Groups theory and the problems found on the formulation of Relativistic Quantum Mechanics, the student will comprehend the motivations behind the quantum version of the field theory, while he developments the analytic and computational tools needed to a Project of theoretical physics. In particular, these tools will be first used to a detailed study of Quantum Electrodynamic, and then later focus on Yang-Mills theories with non-abelian symmetry groups. The emphasis will be on both importance and difficulties of the quantization of vector fields due Gauge Invariance, and on calculation of relevant quantities for phenomenology. The final objective is to give the student all the tools needed to write a Lagrangian invariant to any Lie Symmetry group. In particular, the student shall calculate the cross section of the gluon scattering, gg ’ gg, of the chromodynamics (this calculation involves both group theory as quantum field theory). (AU)