The Algebra & Geometry of Modern Physics

The aim of the talk is to formulate – after Chevalley – an algebraic concept of a spinor associated with a given quadratic space and its Clifford algebra. To this end, representations of a Clifford algebra will be introduced, the Clifford group and its Pin and Spin subgroups will be defined and related to the orthogonal group of the quadratic space. Finally, the spin representation of the Clifford algebra will be constructed, and – time permitting – its distinguished place in the representation theory of the Clifford algebra will be indicated. An explicit construction of Cartan's geometric spinors associated with an isotropic subspace in a real pseudoeuclidean space will be detailed and related to Chevalley's algebraic spinors.