The structure of : preliminaries

It remains to explain what is .

We have to remember the -covariance condition (4) on . It implies that the construction of should be covariant under the local Lorentz transformations . It is convenient to consider complexified symmetry algebras: and . The spinors transform in the fundamental representation of and antifundamental of :


The is characterized as the subalgebra preserving the symplectic forms and , which are both given by the -matrices


This allows to write covariant chains of letters and linked with , for example: