  We explore some general consequences of a proper, full enforcement of the
"twisted Poincare'" covariance of Chaichian et al. [14], Wess [50], Koch et al.
[34], Oeckl [41] upon many-particle quantum mechanics and field quantization on
a Moyal-Weyl noncommutative space(time). This entails the associated braided
tensor product with an involutive braiding (or $\star$-tensor product in the
parlance of Aschieri et al. [3,4]) prescription for any coordinates pair of
$x,y$ generating two different copies of the space(time); the associated
nontrivial commutation relations between them imply that $x-y$ is central and
its Poincar\'e transformation properties remain undeformed. As a consequence,
in QFT (even with space-time noncommutativity) one can reproduce notions (like
space-like separation, time- and normal-ordering, Wightman or Green's
functions, etc), impose constraints (Wightman axioms), and construct free or
interacting theories which essentially coincide with the undeformed ones, since
the only observable quantities involve coordinate differences. In other words,
one may thus well realize QM and QFT's where the effect of space(time)
noncommutativity amounts to a practically unobservable common noncommutative
translation of all reference frames.
