Introduction

In this chapter we will consider some major problems in quantum field theory. They are related to the understanding of polarisation effects in the vacuum state. Although this state in the mean is empty it nevertheless embraces the continuous production and annihilation of virtual particle-antiparticle pairs due to quantum fluctuations. All the real charges and currents then behave as if they were moving in a dielectric medium. In connection with QED this effect is small (although readily observable). For QCD, on the other hand, it plays a major role.

The first kind of problem is mathematical, related to ill-defined series expansions in perturbation theory and also to undefined integrals. The second is general in physics: it is necessary to isolate the effective dependence on the theoretical parameters in all the calculated expressions for the observables (note that this dependence is in general complicated when one deals with non-linear equations). This is the renormalisation procedure, which always must be performed in order to relate the parameters in a theoretical expression to the observables in an experiment.

It is true that physicists are, compared to most other scientists, privileged because the components of many systems in physics can be isolated. In this situation the properties of each component can be determined. Afterwards the whole system can be brought back into interaction, with well-defined values of the parameters which govern the behaviour of each subsystem.