  This paper is an {\sf application} to Einstein's gravity (EG) of the
mathematics developed in A. Plastino, M. C. Rocca: J. Phys. Commun. {\bf 2},
115029 (2018). We will quantize EG by appeal to the most general quantization
approach, the Schwinger-Feynman variational principle, which is more
appropriate and rigorous that the functional integral method, when we are in
the presence of derivative couplings \nd We base our efforts on works by Suraj
N. Gupta and Richard P. Feynman so as to undertake the construction of a
Quantum Field Theory (QFT) of Einstein Gravity (EG). We explicitly use the
Einstein Lagrangian elaborated by Gupta \cite{g1} but choose a new constraint
for the theory that differs from Gupta's one. In this way, we avoid the problem
of lack of unitarity for the $S$ matrix that afflicts the procedures of Gupta
and Feynman. Simultaneously, we significantly simplify the handling of
constraints. This eliminates the need to appeal to ghosts for guarantying the
unitarity of the theory. Our ensuing approach is obviously non-renormalizable.
However, this inconvenience can be overcome by appealing tho the mathematical
theory developed by Bollini et al. \cite{tp3,tp18,tp19,tp20,pr} Such
developments were founded in the works of Alexander Grothendieck \cite{gro} and
in the theory of Ultradistributions of Jose Sebastiao e Silva \cite{tp6} (also
known as Ultrahyperfunctions). Based on these works, we have constructed a
mathematical edifice, in a lapse of about 25 years, that is able to quantize
non-renormalizable Field Theories (FT). Here we specialize this mathematical
theory to treat the quantum field theory of Einsteins's gravity (EG). Because
we are using a Gupta-Feynman inspired EG Lagrangian, we are able to evade the
intricacies of Yang-Mills theories.
