# Non-factorisation of Hilbert space in QG If we divide a spatial slice into $\Sigma$ and its complement $\overline{\Sigma}$, it is necessary for the definition of entanglement entropy that the total Hilbert space factorises as$\mathcal{H}=\mathcal{H}_{\Sigma} \otimes \mathcal{H}_{\overline{\Sigma}} .$This is not the case in gauge and gravity theories. ## Refs - [[2005#Giddings, Marolf, Hartle]]: defines pseudi-local observables - [[2015#Giddings]]: algebraic perspective - a simple argument given in [[2016#Donnelly, Freidel]]: any gauge theory has this feature - another approach in [[2013#Casini, Huerta, Rosabal]]