Complex structures and the Elie Cartan approach to the theory of spinors

Details Complex structures and the Elie Cartan approach to the theory of spinors Complex structures and the Elie Cartan approach to the theory of spinors

1992-10-20

arxiv.org/abs/hep-th/9210108v1

Physics

High Energy Physics

High Energy Physics - Theory

10p

Scientific paper

Each isometric complex structure on a 2$\ell$-dimensional euclidean space $E$ corresponds to an identification of the Clifford algebra of $E$ with the canonical anticommutation relation algebra for $\ell$ ( fermionic) degrees of freedom. The simple spinors in the terminology of E.~Cartan or the pure spinors in the one of C. Chevalley are the associated vacua. The corresponding states are the Fock states (i.e. pure free states), therefore, none of the above terminologies is very good.

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