Grassmann and Clifford algebras and their applications in electromagnetism

• Grant number: 06/03314-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2006
• End date: August 31, 2007
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Jayme Morandi Vaz
• Grantee: Danilo Borim do Nascimento
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

We intend to study the Grassmann and Clifford algebras and their applications to electromagnetism. A supervised study of introduction to Grassmann and Clifford algebras will be done having in mind the formulation of Maxwell equations using the Dirac-Kähler-Atiyah operator and a formulation of electromagnetism theory in a space without metric. Our main purpose is to study modern mathematical methods with important applications in physics and applied mathematics and study important aspects of electromagnetic theory hidden in its usual formulation. We believe this project will help to reinforce the mathematical and physical backgrounds of the student and stimulate the interest in research.