Conformal gauge fixing and Faddeev-Popov determinant in 2-dimensional Regge gravity
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By regularizing the conical singularities by means of a segment of a sphere or pseudosphere and then taking the regulator to zero, we compute exactly the Faddeev--Popov determinant related to the conformal gauge fixing for a piece-wise flat surface with the topology of the sphere. The result is analytic in the opening angles of the conical singularities in the interval ($π$, $4π$) and in the smooth limit goes over to the continuum expression. The Riemann-Roch relation on the dimensions of ker$(L^†L)$ and ker$(LL^†)$ is satisfied.
8 pages, latex. Talk given at the XVIII International Workshop on High Energy Physics and Field Theory; Protvino, Russia, June 1995
8 pages, latex. Talk given at the XVIII International Workshop on High Energy Physics and Field Theory; Protvino, Russia, June 1995