Da partícula ao campo: um estudo do campo spinorial e suas simetrias internas

Abstract

This work reviews the Special Theory of Relativity (SRT), addressing the geometric implications of Minkowski spacetime and delving into the mathematical aspects of the Lorentz group (GL). In addition, the wave equation for a relativistic particle is derived, which results in the Dirac equation, which describes particles of spin 1/2. Then, a detailed study is carried out on local symmetries in field theory and their connection with the spinor field. The objective of this teaching material is to provide a clear and accessible understanding of the mathematical tools necessary for the study of relativistic field theories, facilitating both theoretical analysis and the manipulation of the equations that describe the behavior of particles. It is expected that this content will be useful as a complement to the basic bibliography of the area, allowing students beginning in High Energy Physics and Elementary Particle Physics to explore and deepen their knowledge in this challenging and fascinating field. The material therefore aims to assist in the transition from initial learning to a deeper understanding of the complex interactions between particles and fields.