  We study the convergence of the path integral for General Relativity with
matter on a picewise linear (PL) spacetime that corresponds to a triangulation
of a smooth manifold by using a path-integral measure that renders the pure
gravity path integral finite. This measure depends on a parameter p, and in the
case when the matter content is just scalar fields, we show that the path
integral is absolutely convergent for p > 0,5 and not more than 2 scalar
fields. In the case of Yang-Mills fields, we show that the path integral is
absolutely convergent for the U(1) group and p > 0,5. In the case of Dirac
fermions, we show that the path integral is absolutely convergent for any
number of fermions and a sufficiently large p. When the matter content is given
by scalars, Yang-Mills fields and fermions, as in the case of the Standard
Model, we show that the path integral is absolutely convergent for p > 46,5.
Hence one can construct a finite quantum gravity theory on a PL spacetime such
that the classical limit is General Relativity coupled to the Standard Model.
