 Perturbative quantum field theory

Perturbative quantum field theory approximates an interacting quantum field theory by expanding around a solvable reference theory, usually a free field theory. Powers of interaction couplings organize the contributions to correlation functions and scattering amplitudes. Feynman diagrams encode the terms, their internal propagators and their combinatorial factors.

At leading order, tree diagrams often reveal the main process; loop diagrams give quantum corrections. Divergent intermediate expressions require a specified regularization and renormalization prescription before comparison with physical quantities. A small coupling is helpful but is not the only validity condition: large logarithms, thresholds or long evolution can invalidate a fixed-order approximation. Some phenomena, including certain bound states and tunnelling effects, require resummation or methods beyond an ordinary power series.