Faddeev-Popov determinant in 2-dimensional Regge gravity

By regularizing the singularities appearing in the two dimensional Regge calculus by means of a segment of a sphere or pseudo-sphere and then taking the regulator to zero, we obtain a simple formula for the gauge volume which appears in the functional integral. Such a formula is an analytic function of the opening of the conic singularity in the interval from π to 4π and in the continuum limit it goes over to the correct result.