Quantum Field Theory (QFT) distinguishes between weakly and strongly coupled regimes based on whether interaction terms in the Lagrangian are small relative to quadratic free-field terms; this classification dictates the validity of perturbation theory versus non-perturbative phenomena. The Interaction Picture formalizes time evolution by splitting the Hamiltonian into a solvable free part ($H_0$) governing operators and an interaction part ($H_I$) governing state dynamics, resolved through Dyson's formula involving time-ordered exponentials to handle operator non-commutativity at different times. Consequently, physical observables such as scattering amplitudes are extracted via the S-Matrix by computing transition probabilities between asymptotic free states using perturbation expansions in powers of small coupling constants, underpinned by conservation laws and relativistic kinematics defined through delta functions.
Quantum Field Theory (QFT) distinguishes between weakly and strongly coupled regimes based on whether interaction terms in the Lagrangian are small relative to quadratic free-field terms; this classi…