Editing Propagator (section)

===Propagators in Feynman diagrams===
The most common use of the propagator is in calculating [[probability amplitude]]s for particle interactions using [[Feynman diagram]]s.  These calculations are usually carried out in momentum space. In general, the amplitude gets a factor of the propagator for every ''internal line'', that is, every line that does not represent an incoming or outgoing particle in the initial or final state. It will also get a factor proportional to, and similar in form to, an interaction term in the theory's [[Lagrangian (field theory)|Lagrangian]] for every internal vertex where lines meet.  These prescriptions are known as ''Feynman rules''.

Internal lines correspond to virtual particles. Since the propagator does not vanish for combinations of energy and momentum disallowed by the classical equations of motion, we say that the virtual particles are allowed to be [[off shell]]. In fact, since the propagator is obtained by inverting the wave equation, in general, it will have singularities on shell.

The energy carried by the particle in the propagator can even be ''negative''. This can be interpreted simply as the case in which, instead of a particle going one way, its [[antiparticle]] is going the ''other'' way, and therefore carrying an opposing flow of positive energy.  The propagator encompasses both possibilities.  It does mean that one has to be careful about minus signs for the case of [[fermions]], whose propagators are not [[even function]]s in the energy and momentum (see below).

Virtual particles conserve energy and momentum. However, since they can be off shell, wherever the diagram contains a closed ''loop'', the energies and momenta of the virtual particles participating in the loop will be partly unconstrained, since a change in a quantity for one particle in the loop can be balanced by an equal and opposite change in another. Therefore, every loop in a Feynman diagram requires an integral over a continuum of possible energies and momenta. In general, these integrals of products of propagators can diverge, a situation that must be handled by the process of [[renormalization]].