  A particle which lives in a d-dimensional ordinary and a d-dimensional
Grassmann space manifests itself in an ordinary four-dimensional subspace as a
spinor, a scalar or a vector with charges. Operators of the Lorentz
transformations and translations in both spaces form the super- Poincar\' e
algebra. It is the super-Pauli-Ljubanski vector which generates spinors.
Vielbeins and spin connections with the Lorentz index larger than or equal to
five may manifest in a four-dimensional subspace as an electromagnetic, a weak
and a colour field.

High Energy Physics - Theory