Introdução às partículas de Majorana na teoria quântica de campos

Abstract

Majorana particles represent a special class of fermions that fundamentally differ from Dirac particles by being identical to their own antiparticles. This work addresses the mathematical formalism required to understand these objects within the framework of Quantum Field Theory, starting from a review of the Dirac equation and spinor algebra to the explicit construction of the Majorana field. The self-conjugation condition, ψ = ψc, imposes constraints that reduce the number of degrees of freedom and profoundly modify the structure of the theory, allowing mass terms that violate lepton number conservation. The physical implications of these mathematical properties are analyzed, with emphasis on neutrinos as the main experimental candidates. Neutrinoless double beta decay emerges as a decisive test of the Majorana nature, while the see-saw mechanism provides a natural explanation for the small observed masses of these particles. The results demonstrate how conceptual modifications in the description of fermions can lead to experimentally testable phenomenology.