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Grassmann and Clifford algebras and their applications in electromagnetism

Grant number: 06/03314-2
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): September 01, 2006
Effective date (End): August 31, 2007
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Jayme Vaz Junior
Grantee:Danilo Borim do Nascimento
Home 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.