  We study the consequences of twisting the Poincare invariance in a quantum
field theory. First, we construct a Fock 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.
