The transfer matrix in four-dimensional Causal Dynamical Triangulations

TL;DR

This paper introduces a phenomenological transfer matrix model for 4D Causal Dynamical Triangulations, using Monte Carlo simulations to derive an effective action based on spatial volume states, aligning with minisuperspace models.

Contribution

It presents a novel transfer matrix approach focusing on spatial volume states in 4D CDT, bridging quantum states with effective minisuperspace actions.

Findings

Effective transfer matrix elements determined via Monte Carlo

Effective action consistent with minisuperspace models

No degrees of freedom are frozen in the model

Abstract

Causal Dynamical Triangulations is a background independent approach to quantum gravity. In this paper we introduce a phenomenological transfer matrix model, where at each time step a reduced set of quantum states is used. The states are solely characterized by the discretized spatial volume. Using Monte Carlo simulations we determine the effective transfer matrix elements and extract the effective action for the scale factor. In this framework no degrees of freedom are frozen, however, the obtained action agrees with the minisuperspace model.