  We study the spectral representation and dispersion relations that follow
from some basic assumptions and the reduced spacetime symmetries on
noncommutative (NC) space. Kinematic variables involving the NC parameter
appear naturally as parametric variables in this analysis. When subtractions
are necessary to remove ultraviolet divergences, they are always made at the
fixed values of these NC variables. This point is also illustrated by a
perturbative analysis of self-energies. Our analysis of the reduced spacetime
symmetries suggests a weaker microcausality requirement. Starting from it, we
make a first attempt at dispersion relations for forward scattering. It turns
out that the attempt is hampered by a new unphysical region specified by a
given motion in the NC plane which does not seem to be surmountable using the
usual tricks. Implications for a possible subtraction and renormalization
scheme for NC field theory in which the ultraviolet-infrared (UV/IR) mixing is
removed are also briefly commented on.
