Canonical Tensor Model with Local Time and its Uniqueness

TL;DR

This paper introduces a canonical tensor model incorporating local time, demonstrating its algebraic consistency and connection to general relativity, and discusses its quantization.

Contribution

It proposes a new canonical formalism for a rank-three tensor model with local time, establishing its algebraic structure and relation to general relativity.

Findings

Existence of only two local Hamiltonians under certain assumptions

Constraint algebra approaches the DeWitt algebra in a locality limit

Brief discussion on quantization of the model

Abstract

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.