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The peculiarities of doing a canonical analysis of the first orderformulation 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 thedifference between using $g^{\alpha \beta}$ as opposed to $h^{\alpha \beta}$appears only in two spacetime dimensions. Despite there being a differentnumber of constraints in these two approaches, both formulations result inthere being a local Poisson brackets algebra of constraints with fieldindependent structure constants, closed off shell generators of gaugetransformations and off shell invariance of the action. The formulation interms of the metric tensor is analyzed in detail and compared with earlierresults obtained using the metric density. The gauge transformations, obtainedfrom the full set of first class constraints, are different from adiffeomorphism transformation in both cases.Comment: 13 page

PECULIARITIES OF THE CANONICAL ANALYSIS OF THE TWO-DIMENSIONAL FIRST-ORDER EINSTEIN–HILBERT ACTION IN TERMS OF THE METRIC TENSOR OR THE METRIC DENSITY