N ov 1 99 9 Locally Weyl invariant massless bosonic and fermionic spin - 1 / 2 action in the ( Y 4 , g ) space - time .

Locally Weyl invariant massless bosonic and fermionic spin-1/2 action in the (Y 4 , g) space-time. Abstract We search for a real bosonic and fermionic action in four dimensions which both remain invariant under local Weyl transformations in the presence of contortion and non-metricity tensor. In the presence of the non-metricity tensor the investigation is extended to (W n , g) space-time while when the torsion is encountered we are restricted to the (U 4 , g) space-time. Our results hold in general for the (Y 4 , g) space-time and we also calculate extra contributions to the conformal gravity.