The S-matrix maps incoming asymptotic states to outgoing asymptotic states. Its connected transition matrix elements contain an overall energy-momentum Dirac delta function and an invariant scattering amplitude. In quantum field theory, the LSZ reduction formula obtains these elements from amputated field correlators.
The S-matrix, or scattering matrix, is a fundamental concept in quantum mechanics and quantum field theory that describes how the initial states of a physical system evolve into final states through scattering processes. It encapsulates the probabilities of transitioning from one set of quantum states to another due to interactions. In more detail: 1. **Definitions**: The S-matrix relates the "in" states (initial states of particles before interaction) to the "out" states (final states after interaction).
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