Forces between fundamental point particles are described in terms of exchange of bosons, a single boson in first order, two bosons in second order, etc. The exchanged boson is “virtual,” that is, the length of the energy-momentum four-vector is not the usual (mc)² but can be anything. The virtual boson is said to be “off the energy shell.” The Feynman diagram is actually a graphic that, with the help of a set of rules, converts into a matrix element for the process depicted. The fermion lines are free-particle Dirac states, while the intermediate boson line corresponds to a “propagator,” which is basically the operator form of a Green's function.  Each distinct diagram is a bookkeeping device for writing down an integral to be evaluated.

The diagrams offer an easy way to enumerate all the matrix elements that have to be calculated to get a result for the probability of a given kind of process. The technique has proven useful in many other fields of theoretical physics, for example condensed-matter physics.  Each diagram is a term in a perturbation series that sums to give the overall amplitude for a given process.  The problem with such an approach is that the series may not converge, or may converge so slowly that reliable calculations are nearly impossible!  Beware that some people draw diagrams with the x axis being space, while others draw diagrams with the x axis being time.

Fermions are drawn going forward in time, while antifermions are drawn going backward in time. The probability of emission or absorption of a boson is specified by the vertex coupling constant. For example, for the electromagnetic interaction, the vertex coupling constant is the square root of the fine structure constant α. [You might think the γ seen in this diagram is a real, not a virtual, photon. But to satisfy conservation laws, pair-annihilation must produce two photons, so the single photon seen here must in fact be virtual! The boson represented by a spring-like line is a gluon, the boson responsible for the strong force.]

Fundamental particles carrying color, such as quarks and gluons, cannot be observed directly because they cannot propagate more than about 1 fm. What they do is to disintegrate--- in two steps--- into a “jet” of hadrons, that is, a mixture of ordinary (colorless) baryons and mesons. It is the jet that is seen, not the quark or gluon originally “knocked out” in the process.