Noncommutative hamiltonian formalism for noncommutative gravity

TL;DR

This paper develops a covariant canonical formalism for noncommutative gravity using twisted products, generalizing Noether theorems and constructing gauge generators in a noncommutative phase space.

Contribution

It introduces a novel covariant canonical framework for noncommutative gravity and extends Noether theorems to this setting, including the construction of gauge generators.

Findings

Formalism applied to noncommutative 4D vierbein gravity

Canonical generators of the tangent space star-gauge group identified

Generalization of Noether theorems to noncommutative theories

Abstract

We present a covariant canonical formalism for noncommutative gravity, and in general for noncommutative geometric theories defined via a twisted $\star$-wedge product between forms. Noether theorems are generalized to the noncommutative setting, and gauge generators are constructed in a twisted phase space with $\star$-deformed Poisson bracket. This formalism is applied to noncommutative $d=4$ vierbein gravity, and allows to find the canonical generators of the tangent space $\star$-gauge group.