S-matrix

Summary

The S-matrix, or scattering operator, is an operator of scattering theory. It sends the free state of a system long before a collision to its free state long after. Its matrix elements between incoming and outgoing states give the probability amplitudes of all possible outcomes of a collision. Conservation of probability makes it a unitary operator when the theory is asymptotically complete. In quantum field theory it is the main observable of particle physics, and the LSZ reduction formula expresses it through correlation functions.