We study a regularization of the Pauli-Villars kind of the one loop
gravitational divergences in any dimension. The Pauli-Villars fields are
massive particles coupled to gravity in a covariant and nonminimal way, namely
one real tensor and one complex vector. The gauge is fixed by means of the
unusual gauge-fixing that gives the same effective action as in the context of
the background field method. Indeed, with the background field method it is
simple to see that the regularization effectively works. On the other hand, we
show that in the usual formalism (non background) the regularization cannot
work with each gauge-fixing.In particular, it does not work with the usual one.
Moreover, we show that, under a suitable choice of the Pauli-Villars
coefficients, the terms divergent in the Pauli-Villars masses can be corrected
by the Pauli-Villars fields themselves. In dimension four, there is no need to
add counterterms quadratic in the curvature tensor to the Einstein action
(which would be equivalent to the introduction of new coupling constants). The
technique also works when matter is coupled to gravity. We discuss the possible
consequences of this approach, in particular the renormalization of Newton's
coupling constant and the appearance of two parameters in the effective action,
that seem to have physical implications.Comment: 26 pages, LaTeX, SISSA/ISAS 73/93/E
