Tensor models are
generalization of matrix models, and are studied as discrete models for quantum gravity for more than two-dimensions. Among them, the rank-three tensor models can be interpreted as theories of dynamical fuzzy spaces, and they generally have the feature of
respecting symmetries. In this talk, after briefly reviewing some results on Euclidean models such as spontaneous generation of fuzzy spaces and Euclidean general relativity respecting the diffeomorphism symmetry on them, I will present a way to introduce “local” time to the rank-three tensor models by constructing “local” Hamiltonians. The consistency among the multiple ways of local time evolutions is guaranteed by the on-shell closure of the constraint algebra among the
local Hamiltonians and the symmetry generators of the tensor models. The constraint algebra is shown to approach the DeWitt algebra in a formal continuum limit. I will also discuss the two-fold uniqueness of the local Hamiltonians, and will briefly show some preliminary results on the quantization.