Gravitational Field Equations of Fourth Order and Supersymmetry

Abstract

Abstract We discuss the field equations which stem from a variational principle containing the quadratic terms α R μν R μν and β R 2 besides the Einstein‐Hilbert Lagrangian R . Comparison of this theory with a pure theory of fourth order shows that R must necessarily be included if we wish to interpret the field equations as gravitational equations. The Einstein‐Bach‐Weyl theory (α = −3β) has the property of being a theory of “supergravitation”. Apart from gravitons without rest‐mass, we have here only one additional kind of particles with rest‐mass. Their mass may be determined by Planck' slength ( hG/c 3 ) 1/2 . The occurrence of those particles results from the breakdown of a “supersymmetry”, that is of the conform invariance. The Einstein tensor E μν  R μν −1/2 g μν R can be regarded as a source of the gravitons without rest‐mass.