  A canonical formalism of the rank-three tensor model with the notion of local
time is proposed. The consistency of the local time evolution is guaranteed by
imposing that local Hamiltonians and the so(N) kinematical symmetry of the
tensor model should form a first class constraint algebra. By imposing some
physically reasonable assumptions, it is shown that there exist only two such
local Hamiltonians with a slight difference in index contraction. The first
class constraint algebra is shown to approach the DeWitt constraint algebra of
the general relativity in a certain locality limit. Quantization of the system
is briefly discussed.
