First-Order Formulations for Spin-1 Theories

• Grant number: 25/17892-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2025
• End date: October 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Elias Leite Mendonça
• Grantee: Pedro Henrique Silva Souza
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

This undergraduate research project is devoted to the investigation of first-order formulations for spin-1 field theories, with particular emphasis on the reinterpretation of Maxwell electrodynamics in terms of a non-symmetric rank-2 auxiliary field. The central goal is to analyze, through a decomposition into irreducible components, the conditions under which the functional integration over these components reproduces the original theory or its dual formulations.Beyond this specific case, the project aims to provide the student with a structured introduction to classical field theory, to modern algebraic and computational tools (notably the \textit{xAct} package), and to potential extensions of the framework to spin-2 theories inspired by the Palatini approach. In this way, the project offers a conceptually grounded entry point into the Lagrangian formalism of classical field theories, thereby fostering the student's academic development in theoretical physics.