Quick guide to nomenclature: Fundamental particles are of two kinds, fermions and bosons. Fermions are conserved in number, obey the exclusion principle, and have spin-1/2. Bosons are not conserved in number, do not obey the exclusion principle, and (usually) have spin 1. Matter is made of fermions, forces are "made" of bosons.
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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.
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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.]
In Feynman diagrams, photons are usually drawn as wavy lines, gluons are drawn as springs, and weak bosons are drawn as dashed lines.
Fundamental particles carrying
color, such as quarks and gluons, cannot be observed directly
in isolation because they cannot propagate more than about 1
fm. (A fermi, fm, is 10-15 m.) 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. Baryons consist of three valence
quarks, while mesons consist of valence quark-antiquark pairs.
The term "valence" means that the quarks are real particles,
not virtual. The actual number of observable particles inside
baryons like the proton and neutron is infinite, as we shall
see.
