  The pp-wave (Penrose limit) in conformal field theory can be viewed as a
special contraction of the unitary representations of the conformal group. We
study the kinematics of conformal fields in this limit in a geometric approach
where the effect of the contraction can be visualized as an expansion of
space-time. We discuss the two common models of space-time as carrier spaces
for conformal fields: One is the usual Minkowski space and the other is the
coset of the conformal group over its maximal compact subgroup. We show that
only the latter manifold and the corresponding conformal representation theory
admit a non-singular contraction limit. We also address the issue of
correlation functions of conformal fields in the pp-wave limit. We show that
they have a well-defined contraction limit if their space-time dependence
merges with the dependence on the coordinates of the R symmetry group. This is
a manifestation of the fact that in the limit the space-time and R symmetries
become indistinguishable. Our results might find applications in actual
calculations of correlation functions of composite operators in N=4 super
Yang-Mills theory.
