The LSZ reduction formula establishes that S-matrix elements for scattering processes in Quantum Field Theory correspond to the residues of poles located at on-shell momenta ($k^2 = m^2$) within time-ordered correlation functions (Green's functions). Formally, this mechanism relates asymptotic multi-particle states defined by wave packets acting as creation and annihilation operators at temporal limits $t \to \pm\infty$ to the limit of these field-theoretic Green's functions via differential operators $(\Box + m^2)$. As a rigorous theorem within relativistic quantum mechanics, it provides an exact definition for interacting S-matrix elements without relying on perturbation theory or diagrammatic expansions, fundamentally linking observable scattering amplitudes to intrinsic vacuum correlators.
The LSZ reduction formula establishes that S-matrix elements for scattering processes in Quantum Field Theory correspond to the residues of poles located at on-shell momenta ($k^2 = m^2$) within time…