Moyal product for (n – 1)-forms within the covariant Hamiltonian formalism for fields

In these brief notes we analyze an associative product for (n – 1)- forms in the polymomentum phase space which is necessary in order to complete the deformation quantization scheme within the context of the multisymplectic formalism. In particular, we identify certain conditions that the proposed product must follow to generate a Moyal bracket induced from the Gerstenhaber bracket naturally emerging within this context. (paper)