The S-Matrix serves as the unitary operator relating asymptotic free particle states in the distant past to those in the distant future within Quantum Field Theory, effectively encoding interaction dynamics through perturbative expansions via Dyson's Series. This formulation relies on defining a unique vacuum and splitting the Hamiltonian into time-independent free and interacting components to construct an Interaction Picture where field observables evolve explicitly with respect to spacetime coordinates. The theoretical framework demonstrates that while local correlation functions describe general quantum processes, the S-Matrix represents specific matrix elements derived from these correlators in the limit of vanishing interaction strength at asymptotic times, providing a rigorous definition for observable scattering amplitudes independent of operator redefinition ambiguities prevalent in interacting theories without conformal symmetry.
The S-Matrix serves as the unitary operator relating asymptotic free particle states in the distant past to those in the distant future within Quantum Field Theory, effectively encoding interaction d…