Chapter V Interacting Fields Lecture 3 Books Recommended: Lectures on Quantum Field Theory by Ashok Das Advanced Quantum Mechanics by Schwabl

S-matrix At , initially particles are far apart And non-interaction Initial state: Then particle come close and interact for Short period and then after long time they again are observed. Particles at

Transition amplitude to final state Scattering matrix or S matrix

In terms of Hamiltonian density S matrix is Lorentz invariant quantity. For QED

S-matrix in Unitary Expanding asymptotic states in terms of Complete set of final states

We write last Eq as From above we write Which shows that the unitary of S matrix implies the conservation of probability