In order to analyze the dynamics of CDT quantum gravity using such simulations, a Wick rotation must be performed to convert the complex path integral amplitudes to real Boltzmann weights. This can be achieved by performing an analytic continuation of the asymmetry parameter, by rotating it in the lower half of the complex plane such that $\alpha$ is mapped to $-\alpha$ [@3d4d]. As a consequence, the gravitational path integral becomes a statistical partition function of the form $$\label{partition}
Z=\sum_{T\in \cal{C}}\frac{1}{C(T)}\exp(-S_{\mathrm{Regge}}^{\mathrm{eucl}}(T)),$$ where $\cal{C}$ is the space of all causal, Lorentzian triangulations $T$, $S_{\mathrm{Regge}}^{\mathrm{eucl}}$ the Euclideanized Regge action and $1/C(T)$ the discrete analog of the path integral measure, with $C(T)$ denoting the order of the automorphism group of $T$. In Sec. \[sec:actions\] below we will derive and discuss the explicit functional form of the Regge implementation of the three-dimensional Einstein-Hilbert action in terms of the triangulation data and the coupling constants of the nonfoliated CDT model.

Relaxing the foliation: 1+1 dimensions {#sec:ncdt_2d}
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As a warm-up for the three-dimensional case, we will in this section illustrate our general strategy for relaxing the distinguished foliation by discussing the situation in 1+1 dimensions. The key idea is to add new elementary Minkowskian building blocks, 