5.2 Quantum fields and unification

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Figure 1.34s Richard P. Feynman (1918-1988) Click here for larger image (15.38kb) A character of extraordinary, insight, wit and charm Click here to learn more about Feynman

It was the problem of infinities that really delayed the completion of QED until the late 1940s. At that time, in a burst of post-war activity, a technique called renormalization was developed that made it possible to get at the physical result hidden behind the unphysical infinity. At the same time a simple diagrammatic method was devised that made it much easier to identify and perform the necessary calculations. The problem of infinities was solved by Julian Schwinger (1918-1994), Sin-itiro Tomonaga (1906-1979) and Richard P. Feynman. The last of these was also responsible for the diagrams, which have become known as Feynman diagrams (Figure 1.33).

Figure 1.33 Feynman diagrams of some of the processes that contribute to the scattering of colliding electrons. Each diagram represents a complicated mathematical expression. The wavy lines represent photons. Click here for larger image (7.20kb)

The completion of QED presented physicists with the most precise theory of Nature they had ever possessed. However, by the time that completion had been achieved it was already clear that electromagnetism and gravitation were not the only forces at work in the world. The familiar contact forces you feel when pressing on a surface had long been understood to be nothing more than manifestations of electromagnetism - atoms repelling other atoms that got too close - but the 1930s and 1940s had provided clear evidence of the existence of two other fundamental forces. These new forces were quite powerful, but both were of such short range that they mainly operated within atoms rather than between them. The new forces were called the strong and weak nuclear forces since their effects were most clearly seen in the behaviour of atomic nuclei. The major properties of all four of the fundamental forces are listed in Table 1.1

Force	Strength	Range	Force Carrier
strong	10-1	10-15m	gluon
electromagnetic	10-2	infinite	photon
weak	10-2	10-17m	W and Z bosons
gravitational	10-45	infinite	graviton(?)

Table 1.1 The four fundamental forces. The strengths are roughly those found at high collision energies, and the force carriers are the particles most closely associated with each force. The graviton is followed by a question mark because its existence is still in doubt.

Formulating quantum field theories of each of the four fundamental forces was an obvious goal, and remains so to this day. Three of the forces - the strong, the weak and the electromagnetic - have been treated with great success; and have been combined to form a so-called standard model of fundamental forces. However, gravity has resisted all attempts to fit it into the same kind of theoretical strait-jacket and seems to require very special treatment if it is to be treated as a quantum field theory at all. If it were not for the problem of gravity we would be able to say that the physicist's current world-view is that the Universe consists of a set of mutually interacting quantum fields that fill the space-time described by special relativity. But it seems that this will not do.

A way forward may be indicated by the standard model itself. The standard model is actually something more than a description of three of the four fundamental forces; it is also to some extent a prototype for their union. Within the standard model the electromagnetic and weak forces appear as a unified electroweak force. The exact meaning of unification in this context is too technical to go into here, but suffice it to say that, under unification, the quantum fields responsible for the weak and electromagnetic forces combine in a way that is slightly reminiscent of Einstein's fusion of space and time to form space-time.
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