Second Quantisation: From Particles to Fields
It was shown in the chapter 4 that fluctuations of quantum fields are particles. The phonons in the solid state physics are a classical example: they are quanta of the crystal lattice vibrations. However, electrons or other elementary particles seem to be logically more primary than any field. Formally, one may introduce a field that upon quantization gives rise to the particles which really exist in our World. The field that possess the desired properties can be used as a theoretical object justified by the comparison of its predictions with experiment. This is possible in principal, but it is not strightforward. In this chapter, we would like to describe another method of second quantisation in which the elementary particles are considered as primary objects and the quantum field as a result. This approach allows us not only to complete logically the second quantisation presented in chapter 6, but also to introduce fermionic fields in a very natural way.