Costa De Beauregard, O.
(1992)
*Quantization of gravity.*
Accademia Peloritana dei Pericolanti Classe FF.MM.NN., 70.
pp. 5-21.

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## Abstract

We 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.

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