  We show the twisted Galilean invariance of the noncommutative parameter, even
in presence of space-time noncommutativity. We then obtain the deformed algebra
of the Schr\"odinger field in configuration and momentum space by studying the
action of the twisted Galilean group on the non-relativistic limit of the
Klein-Gordon field. Using this deformed algebra we compute the two particle
correlation function to study the possible extent to which the previously
proposed violation of the Pauli principle may impact at low energies. It is
concluded that any possible effect is probably well beyond detection at current
energies.
