Clifford algebras, covariant bilinears and singular spinors

• Grant number: 16/14021-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2016
• End date: September 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Roldão da Rocha
• Grantee: Aquerman Yanes Martinho
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

From the fundamental concepts of Clifford algebras and their representations, we shall investigate the rotation group and its double covering, introducing classical spinor in Minkowski spacetime. The main aim of this project is to introduce the fundamentals related to the Spin groups, in particular those ones related to the Minkowski spacetime and, further, to investigate some subsequent properties that carry those group representations. Subsequently we shall investigate the bilinear covariants associated with those spinors, after equivalently defining such objects. We shall construct the bilinear covariants and study the Fierz aggregate, the Fierz identities and their generalizations for the case of singular spinors, that have prominent importance in the literature of the last decade. Moreover, flagpole and flag-dipole structures will be studied. The implementation and fullfilment of this project endows the student with fundamental concepts involving Clifford algebras and their representations, together with the periodicity theorem and subsequent applications.