Messanae Universitas Studiorum: No conditions. Results ordered -Date Deposited. 2017-05-25T10:42:49ZEPrintshttp://cab.unime.it/images/sitelogo.pnghttp://cab.unime.it/mus/2012-09-20T10:13:08Z2012-09-20T10:13:08Zhttp://cab.unime.it/mus/id/eprint/720This item is in the repository with the URL: http://cab.unime.it/mus/id/eprint/7202012-09-20T10:13:08ZQuantization of gravityWe show that, in the Riemannian theory of gravity, the superpotential of the Riemann-Christoffel tensor (the existence of wich stems from the Bianchi identities)is none else than the tensor generalization $V_i_j$ of Poisson's potential, the source of wich is the "material tensor" $T_i_j.$ Endowing then the gravition with a rest mass $c^-^1 \hbar\kappa,$ we see that $\kappa^2 \ V_i_j$ add to $\chi \ T_i_j,$ and is thus interpretable as an energy monumentum density of the gravity field. This allows us to quantize the coupled massive gravition and Proca or Kemmer spin 0 particle fields, by extending into Riemannian geometry the procedure Schwinger used in quantum electrodynamics. Finally, Einstein's gravity tensor $R_i_j- \frac{1}{2}Rg_i_j$ is equated to the mean value $\mathcal{h}\Psi|\chi\tau_i_j+\kappa^2V_i_j|\Psi\mathcal{i}$ of the total energy-momentum density; $\tau_i_j$ denotes the canonical energy-momentum ensity, which is symmetric in the absence of an electromagnetic field.O. Costa De Beauregard