A space of supertwistors is introduced as a graded vector space by starting with ordinary twistor space multiplied with even Grassmann coefficients and combining it by an othogonal direct sum with a one‐dimensional space multiplied with odd Grassmann coefficients. A treatment of the algebraic properties of supertwistor space and of Grassmann‐linear transformations on this space lead to a systematic procedure for deriving the structure equations for the graded Lie algebra su (2,2/1).

Supertwistor realization of SU(2,2/1)

We present an account of the development of supergravity in México.

http://www.ifm.umich.mx/~villasen/AIP-Com_Vol/025-Obregon.pdf

Developments in Supergravity

A differential geometrical approach to n-dimensional spinor algebra is presented by means of which the basic concepts of spinor transformations, Clifford algebras, bilinear inner products on spinor space, and conjugate operations are defined in an intrinsic and compact manner. The relations with Cartan’s theory are established and some generalizations are discussed.

Spinors from a Differential Geometric Point of View

A gauge theory of supergravity which allows one to obtain first‐order Lagrangians that are locally gauge invariant by construction is presented. The formalism makes use of supertwistors as a representation space for the construction of a typical fiber of a vector bundle associated with a principal bundle, where the structural group is the super‐Poincare group. The approach proposed provides a means of resolving one of the central problems of gauge field theories of external symmetry groups, that is the satisfactory treatment of translations.

C. P. Luehr

Papers

Supertwistor fiber bundles as a formalism for supergravities