Functional integration for Regge gravity

A summary is given of recent exact results concerning the functional integration measure in Regge gravity.Comment: 9 pages, AMSLaTex file; talk given at the Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, 17-21 September 199

Functional integration on Regge geometries

We adopt the standard definition of diffeomorphism for Regge gravity in D=2 and give an exact expression of the Liouville action in the discretized case. We also give the exact form of the integration measure for the conformal factor. In D>2 we extend the approach to any family of geometries described by a finite number of parameters. The ensuing measure is a geometric invariant and it is also invariant in form under an arbitrary change of parameters.Comment: 3 pages, LaTeX file. Talk presented at LATTICE96(gravity

Functional determinants by contour integration methods

We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a second order differential operator with Dirichlet boundary conditions. The method is applicable to more general situations, and we discuss the way in which the formalism has to be developed to cover these cases. In particular, we also show that simple and elegant formulae exist for the physically important case of determinants where zero modes exist, but have been excluded.Comment: 29 page

Functional integration and abelian link invariants

The functional integral computation of the various topological invariants, which are associated with the Chern-Simons field theory, is considered. The standard perturbative setting in quantum field theory is rewieved and new developments in the path-integral approach, based on the Deligne-Beilinson cohomology, are described in the case of the abelian U(1) Chern-Simons field theory formulated in S^1 x S^2.Comment: 20 pages, 4 figures, Contribution to the Proceedings of the workshop "Chern-Simons Gauge theory: 20 years after", Bonn, August 200