  The peculiarities of doing a canonical analysis of the first order
formulation of the Einstein-Hilbert action in terms of either the metric tensor
$g^{\alpha \beta}$ or the metric density $h^{\alpha \beta}= \sqrt{-g}g^{\alpha
\beta}$ along with the affine connection are discussed. It is shown that the
difference between using $g^{\alpha \beta}$ as opposed to $h^{\alpha \beta}$
appears only in two spacetime dimensions. Despite there being a different
number of constraints in these two approaches, both formulations result in
there being a local Poisson brackets algebra of constraints with field
independent structure constants, closed off shell generators of gauge
transformations and off shell invariance of the action. The formulation in
terms of the metric tensor is analyzed in detail and compared with earlier
results obtained using the metric density. The gauge transformations, obtained
from the full set of first class constraints, are different from a
diffeomorphism transformation in both cases.
