The transfer matrix in four-dimensional CDT

TL;DR

This paper investigates the transfer matrix in 4D Causal Dynamical Triangulation (CDT) quantum gravity, demonstrating how an effective transfer matrix based on the scale factor can be derived from simulations and linked to an effective minisuperspace action.

Contribution

It introduces an effective transfer matrix for 4D CDT based on the scale factor, connecting simulation results to an effective minisuperspace action.

Findings

Effective transfer matrix elements are determined from simulations.

The matrix elements are well described by an effective minisuperspace action.

The transfer matrix uniquely determines the CDT theory.

Abstract

The Causal Dynamical Triangulation model of quantum gravity (CDT) 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 labeled 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.