Hamiltonian embedding of the massive noncommutative U(1) theory

We show that the massive noncommutative U(1) theory can be embedded in a gauge theory by using the Batalin, Fradkin. Fradkina, and Tyutin Hamiltonian formalism. By virtue of the peculiar non-Abelian algebraic structure of the noncommutative massive U(1) theory, several specific identities involving Moyal commutators had to be used in order to make the embedding possible. This leads to an infinite number of steps in the iterative process of obtaining first-class constraints. We also show that the involutive Hamiltonian can be constructed.