Faddeev-Popov determinant in 2-dimensional Regge gravity.
Pietro Menotti, Pier Paolo Peirano
TL;DR
This paper derives a simple, analytic formula for the gauge volume in 2D Regge gravity by regularizing singularities and taking a continuum limit, aiding in understanding the path integral measure.
Contribution
It introduces a regularization method for singularities in 2D Regge calculus and provides an explicit formula for the gauge volume in the functional integral.
Findings
The formula is an analytic function of the conic singularity opening.
The regularization approach yields the correct continuum limit.
The method simplifies the calculation of gauge volumes in 2D quantum gravity.
Abstract
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 to and in the continuum limit it goes over to the correct result.
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