## Quantum electrodynamics

Quantum electrodynamics (QED) was not a new theory, it was initially developed in 1929 to describe the interaction of light and matter. In particular, light photons interact not with matter as such, but with electrons, which are fundamental carriers of electric charge.

In 1929, Paul Dirac incorporated the theory of special relativity into quantum mechanics, and developed a relativistic theory of the electron. The theory says that the electron has a magnetic moment, which means that it behaves like a little magnet, and interacts with magnetic fields. The strength of that magnetic moment in especially chosen units was exactly 1. Experiments showed that this prediction was very nearly correct. In 1948 very accurate measurements gave a very slight but significant deviation from the predicted value, giving a value 1.00118 with a tiny experimental error of 3 in the last place of decimals. The deviation, it was concluded, was due to the interaction of electrons with light.

Feynman's formalism not only predicted this deviation, but predicted its value with fantastic accuracy. The calculated magnetic moment was 1.00115965246, compared to the very accurate experimental value of 1.00115965221. The accuracy of these numbers can be compared to the thickness of a human hair in a distance from London to New York!

In the theory of quantum electrodynamics the force between electric charges is communicated through the exchange of virtual photons. It combines the following three basic-actions: 'an electron can emit a photon', 'an electron can absorb a photon' and 'a photon can go from place to place'. The process is represented by a diagram invented by Feynman and is illustrated in Figure 14.15.

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Figure 14.15 Feynman diagram illustrating photon exchange between two electrons which gives rise to the electromagnetic force between them.

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Figure 14.15 Feynman diagram illustrating photon exchange between two electrons which gives rise to the electromagnetic force between them.

Feynman diagrams illustrate what is an extremely complex process in a deceptively simple way. Let us take as an example these three Feynman diagrams:

We are considering the possible ways in which we can go from the state with two electrons, one at point 1 and one at point 2 in space-time, and finish with one electron at point 3 and one at point 4. There are many ways in which this can happen. First of all, they may 'ignore' one another and go directly from 1 to 3 and from 2 to 4; alternatively, there is the 'cross-over way', from 1 to 4 and from 2 to 3. We have not bothered to draw diagrams for these.

The first two Feynman diagrams refer to ways in which the electrons go to some intermediate points 5 and 6, exchange a photon, and then continue to either 3 or 4. The third diagram represents a process in which two photons are exchanged.

The complexity of the problem arises in that the intermediate points can be anywhere in space-time. In each diagram the amplitudes for all these routes have to be calculated and added.

As Feynman points out: 'There are billions of tiny arrows which have to be added together, that's why it takes four years of graduate work for students to learn how to do this efficiently... but when you are a graduate student you have got to get your degree so you keep on going.'

The task is not hopeless, however. The more junctions in the diagram, the smaller the amplitude. The probability rapidly decreases to one part in a million and even much smaller, and soon the more complicated ways can be ignored. Computers can be programmed to help (many of the calculations are repetitive, ideal for computers).

Once the method has been mastered, the rewards are great. Quantum electrodynamics has proved to be a most beautiful theory, giving predictions which agree with experiment and results with accuracy which is unprecedented.

Richard Feynman, together with Julian Schwinger and Sin-Itiro Tomonaga, won the Nobel Prize in 1965 for 'their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles'.

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