2.1 The electromagnetic interaction

The electromagnetic field is most conveniently described by a vector potential A and a scalar potential φ. For simplicity, we consider only the potential φ (r, t). Using Maxwell's equations, this may be chosen to satisfy the wave-equation

Here p(r, t) is the electric charge density due to the charged particles, which in atomic and nuclear physics will usually be electrons and protons, and c is the velocity of light. In regions where p = 0, equation (2.1) has solutions in the form of propagating waves; for example, the plane wave

The wave velocity is therefore c, as we should expect. In quantum theory, unlike classical theory, the total energy and momentum of the wave are quantised, and can only be integer multiples of the basic quantum of energy and momentum given by the de Broglie relations:

Such a quantum of radiation is called a photon. A macroscopic wave can be considered to be an assembly of photons, and we can regard photons as particles, each carrying energy E and momentum p.

Using (2.4) and (2.5), E and p are related by For a particle of mass m, the Einstein equation gives