Introduction to spinor and twistor theory

• Grant number: 22/02663-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2022
• End date: December 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Daniel Augusto Turolla Vanzela
• Grantee: Juan Vitor Oliveira Pêgas
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This undergraduate research project aims at providing the candidate with a solid basis on advanced geometrical tools in use in theoretical physics, particularly on those which naturally arise in metric theories of gravity - like General Relativity (GR). Since the candidate has already been introduced to the formalism of GR, this project focuses on the construction of the most general fields complying with the principle of general covariance in curved spacetimes: spinors. Once this is achieved, the candidate will proceed with his studies by approaching twistor theory. This latter topic was originally thought of as a possible framework to quantize gravity. However, its use has extrapolated the area of Physics and found application in pure mathematical areas such as differential/integral equations and geometry (among others). Hence, we believe that this project will greatly improve the candidate's mathematical repertoire, useful to any area of theoretical physics which he might choose to follow in his graduate studies.(AU)