Spin and Clifford algebras, an introduction

M. Lachièze-Rey (1)

1 APC - Cosmologie

In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the link between the two approaches. Finally, we give some notions of the generalisations to arbitrary spacetimes, by the introduction of the spin and spinor bundles.

Mots clés: Clifford algebra; spin; spinor; group theory

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

M. Lachièze-Rey. Spin and Clifford algebras, an introduction. 7th International Conference on Clifford Algebras and their Applications, May 2005, Toulouse (France), France. pp.687-720, ⟨10.1007/s00006-009-0187-y⟩. ⟨hal-00502337⟩