  It is proved that a Poincare invariant Wightman function which fulfils the
spectral property and can be defined at sharp times is local if and only if the
integration over both the energy variables of a commutator in momentum space is
a polynomial in the momentum conjugated to the spacial difference variable of
the commutator with distributional coefficients depending on the remaining
energy and momentum variables. Using this characterisation of locality in
momentum space, the locality of a sequence of Wightman functions with
nontrivial scattering behaviour (associated to some quantum field in indefinite
metric) can be proved by explicit calculations. We compare the above
characterisation of locality with the classical integral representation method
of Jost, Lehmann and Dyson.
