Symmetries in particle physics

• Grant number: 22/07826-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2022
• End date: July 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Tereza Cristina da Rocha Mendes
• Grantee: Artur Soares Rodrigues
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Making a study of mathematical texts and introductory references in theoretical particle physics, we will verify the importance of an approach in terms of group theory and symmetries to obtain an overview of this research area. Additionally, a computational application will be made, considering the Ising Model as an example of spontaneous symmetry breaking, through Monte Carlo numerical simulation. Next, as an alternative to the usual description of quantum mechanics, the Feynman path-integral approach will be studied, which consists of weighing all the possibilities of trajectories of a particle between two points, taking into account the probability distribution for the different trajectories. As a result, a clearer connection to the limit of classical mechanics is obtained, as well as a more flexible quantum formulation, which can be extended to the study of quantum field theories. Subsequently, following the article "Lattice QCD for Novices", the project will approach in an introductory way some aspects of the formulation of Quantum Chromodynamics (QCD) on the lattice, which is based on discretizing the theory in Euclidean space-time, making the corresponding Feynman integrals computable, through the Monte Carlo method.(AU)