The LSZ reduction formula, named after Lüders, Steinweg, and Ziman, is a fundamental result in quantum field theory (QFT) that relates S-matrix elements to time-ordered correlation functions (or Green's functions). It provides a method for calculating the S-matrix (which describes the scattering processes) from the theoretical correlation functions computed in a given quantum field theory.
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The LSZ reduction formula obtains an S-matrix element from a time-ordered correlation function by amputating external propagators, taking external momenta on shell, and multiplying by pole-residue factors and external wavefunctions.