3 - Particles of Spin Zero

Summary

Perhaps a natural reaction to the title of this chapter is that it should be rather short. In condensed matter physics we are interested in the particles that make up the world. They are the protons, neutrons and electrons, of course, and they all have spin 1/2. A few particles, such as the pi-meson, which we come across in particle physics do have spin zero, but they only exist for a very brief time before decaying, so how much can be said that is relevant to condensed matter physics?

This point can actually be answered rather easily. The generalization of quantum mechanics to include relativity is, to say the least, a nontrivial problem. As we shall see, spin-1/2 particles are well described by the Dirac equation. That equation describes both the relativistic nature of the particles and their spin (although the two are not really divisible). Treating spin-zero particles first means we can understand many aspects of the relativistic nature of quantum theory without the added complication of spin. Furthermore, formulae derived in this chapter can be compared with those in later chapters to give added insight into the nature of spin. This is particularly true when we look at the properties of a mythical spin-zero electron in a central Coulomb potential.