Causal Dynamical Triangulation
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Causal Dynamical Triangulations: a lattice theory of quantum gravity
Classical General Relativity (GR) is defined as a
metric theory by the Einstein-Hilbert (EH) action
\begin{equation}
S[g_{\mu\nu};G,\Lambda] =
\frac{ 1}{16 \pi G}\int d^4 x \sqrt{-g(x)} \, \Big( R(x) - 2 \Lambda\Big), \tag{1}
\end{equation}
where $G$ denotes the gravitational constant, $\Lambda$ the cosmological constant and
where $c = \hbar =1$ units are used. $g_{\mu\nu}$ is the four-metric of
spacetime and $g$ the determinant of $g_{\mu\nu}$. The corresponding quantum
theory is formally defined by the path integral
\begin{equation}
Z(G,\Lambda) = \int {\cal D} [g_{\mu\nu}] \; e^{iS[g_{\mu\mu};G,\Lambda]} \tag{2}
\end{equation}
