Canonical formulation of a bosonic matter field in (1+1)-dimensional curved space

We study a bosonic scalar in (1 + 1)-dimensional curved space that is coupled to a dynamical metric field. This metric, along with the affine connection, also appears in the Einstein Hilbert action root-gg(mu nu) R-mu nu(Gamma) when written in first-order form. After applying the Dirac constraint formalism to the Einstein Hilbert action and the action of the bosonic scalar field separately, we apply it to these actions when they are combined. Only in the latter case does a dynamical degree of freedom emerge.