Speaker
Description
Abstract:
In a recent paper, A. D’Adda has shown that assigning a length to each link and coordinates to each labelled vertex it is possible to fix a non-Euclidean flat metric and a reference frame in each simplex invariant under GL(n,R). The metric tensor is function of the link lengths and of the coordinates of the vertices. We will show that by performing a gauge-fixing on the metric tensor, we can succeed in calculating the Fadeev-Popov determinant for the Quantum Measure of the Regge Calculus. This has been a longstanding problem that we hope to contribute to understand. This could have important consequences for numerical simulations of Quantum Regge Calculus and for Dynamical Triangulations and, probably, for Causal Dynamical Triangulations.
D’Adda has shown that by assigning a length to each link and coordinates to each labelled vertex, one can define a non-Euclidean flat metric and a reference frame within each simplex that is invariant under . In this formulation, the metric tensor is a function of both the link lengths and the vertex coordinates.
In this talk, we show that by performing an appropriate gauge fixing of the metric tensor, it is possible to compute explicitly the Faddeev–Popov determinant entering the quantum measure of Regge calculus. The determination of this measure has been a longstanding open problem, and our results represent a step toward its resolution.
A well-defined quantum measure has important implications for numerical investigations of quantum gravity. In particular, our approach may lead to improved simulations in Quantum Regge Calculus and could also have consequences for Dynamical Triangulations and, potentially, for Causal Dynamical Triangulations.