  A multiparticle system produced by a large number of independent sources is
described by a gaussian density matrix W. All theoretical approach to
Bose-Einstein Correlatios Cn in high energy physics use this form for W. One of
the most salient consequences of this form is the fact that all higher order
(n>2) moments of the current distribution can be expressed in terms of the
first two. We test this property by comparing the data on C2(Q^2), C3(Q^2) and
C4(Q^2) from pion-p and K-p reactions at 250 GeV/c with the predictions of a
general quantum statistical space-time approach. Even a simplified version of
such approach can account for the data. Previous attempts along these lines,
which did not use the space-time approach, met with difficulties.
