The Transfer Matrix in Four-Dimensional Causal Dynamical Triangulations

Abstract

Abstract.The Causal Dynamical Triangulation model of quantum gravity (CDT) is a proposition to evaluate the path integral over space-time geometries using a lattice regularization with a discrete proper time and geometries realized as simplicial manifolds. The model admits a Wick rotation to imaginary time for each space-time configuration. Using computer simulations we determined the phase structure of the model and discovered that it predicts a de Sitter phase with a four-dimensional spherical semi-classical background geometry. The model has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labelled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.

Differentiable-path integrals in quantum mechanics

“…Causal Dynamical Triangulation. It has also been proposed, specially in the context of quantum gravity, the possibility of summing only over space-time histories (paths) which always lie inside their local light cone [27][28][29][30]. Some of them assume a discrete space-time in order to regularize the UV divergences.…”

An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus

“…The Transfer Matrix in a Quasiclassical Approximation with Constant and Position-Dependent Mass and Resonant Tunneling is given in [23]. The Transfer Matrix in four-dimensional Causal Dynamical Triangulations is presented in [24], and in [25] is given a Transfer Matrix optimization of a one-dimensional photonic crystal cavity for enhanced absorption of monolayer graphene.…”