In quantum field theory, the transition amplitude is a complex number computed via the path integral formalism (summing the action-weighted contributions of all possible field configurations connecting an initial and final state) that determines the probability of a system transitioning from one quantum state to another. Bhabha scattering — the electron-positron scattering process mediated by a virtual photon — serves as a canonical example for expressing transition amplitudes through creation and annihilation operators acting on Fock states, illustrating core QFT machinery including Feynman propagators, orthogonality of multi-particle states, and the distinction between particle-theory (non-relativistic/relativistic quantum mechanics) and field-theory (QFT) formulations.
In quantum field theory, the transition amplitude is a complex number computed via the path integral formalism (summing the action-weighted contributions of all possible field configurations connecti…