Initial and final state radiation

The Initial and Final States of the interaction relate through the so-called scattering matrix (S-matrix).

In analogy with bremsstrahlung, if the radiation is electromagnetic it is sometimes called beam-strahlung, and similarly can have gluon-strahlung (as shown in the Feynman figure with the gluon) as well in the case of QCD.

In these simple cases, no automatic calculation software packages are needed and the cross-section analytical expression can be easily derived at least for the lowest approximation: the Born approximation also called the leading order or the tree level (as Feynman diagrams have only trunk and branches, no loops).

Interactions at higher energies open a large spectrum of possible final states and consequently increase the number of processes to compute, however.

More precisely, and technically, a Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory.

Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative S-matrix.

The transition amplitude is then given as the matrix element of the S-matrix between the initial and the final states of the quantum system.