  We consider the path integral of a quantum field theory in Minkowski
spacetime with fixed boundary values (for the elementary fields) on asymptotic
boundaries. We define and study the corresponding boundary correlation
functions obtained by taking derivatives of this path integral with respect to
the boundary values. The S-matrix of the QFT can be extracted directly from
these boundary correlation functions after smearing. We interpret this relation
in terms of coherent state quantization and derive the constraints on the
path-integral as a function of boundary values that follow from the unitarity
of the S-matrix. We then study the locality structure of boundary correlation
functions. In the massive case, we find that the boundary correlation functions
for generic locations of boundary points are dominated by a saddle point which
has the interpretation of particles scattering in a small elevator in the bulk,
where the location of the elevator is determined dynamically, and the S-matrix
can be recovered after stripping off some dynamically determined but non-local
``renormalization'' factors. In the massless case, we find that while the
boundary correlation functions are generically analytic as a function on the
whole manifold of locations of boundary points, they have special singularities
on a sub-manifold, points on which correspond to light-like scattering in the
bulk. We completely characterize this singular scattering sub-manifold, and
find that the corresponding residues of the boundary correlations at these
singularities are precisely given by S-matrices. This analysis parallels the
analysis of bulk-point singularities in AdS/CFT and generalizes it to the case
of multi-bulk point singularities.
