Twisted coalgebra structure of Poincaré group and noncommutative QFT on the moyal space

We study the consequences of twisting the coalgebra structure of Poincaré group in a quantum field theory on a flat space-time. First, we construct a tensor product representation space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.