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

The S-matrix and boundary correlators in flat space