  We introduce a way to compute scattering amplitudes in quantum field theory
including the effects of particle production and detection. Our amplitudes are
manifestly causal, by which we mean that the source and detector are always
linked by a connected chain of retarded propagators. We show how these
amplitudes can be derived from a path integral, using the Schwinger-Keldysh
"in-in" formalism. Focussing on phi-cubed theory, we confirm that our approach
agrees with the standard S-matrix approach in the case of positive energy
plane-wave scattering.
