What is a covariant derivative?

Abstract

A slight change of emphasis, from geometry towards local symmetry, provides a better framework for the formulation of gauge theories of the gravitational type. General Relativity no longer requires any improvisation, whether the local algebra is based on Poincaré or on De Sitter. Application to the graded super Minkowski manifold, with local algebra based on the super Poincaré algebra, leads to an action principle. The torsion constraints are obtained by straightforward variation of the action . The comparison with component supergravity has not yet been completed, but preliminary indications strongly indicate a close relationship. Local symmetry of the action principle is maintained, the structure is field independent, and the torsion constraints also preserve the local symmetry algebra. The coupling to matter shows that these constraints are necessary for the exclusion of ghosts from the matter sector.