Charges in Gauge Theories

The standard model of particle physics describes three forces: electromagnetism, the weak nuclear interaction and the strong nuclear force. Each of them is described by a gauge theory: that of electromagnetism is an abelian theory, while the other two are non-abelian. The gauge symmetry of the weak interaction is, however, hidden: we say that it is spontaneously broken. Each interaction has a type of charge associated with it. The so-called colour charge of the strong force is, though, never seen. Particles and fields with colour charges are said to be confined inside colourless hadrons (particles like the proton).
The masses of hadrons may be understood in term of their being made out of building blocks, called constituent quarks. A fundamental problem in strong interaction physics is to explain how these particles can emerge from the underlying gauge theory. Our programme for understanding the constituent nature of hadrons has made many advances here.

A fundamental consequence of the gauge symmetries of the standard model is that physics must be gauge invariant. Thus any description of charged particles, such as the electron, has to be gauge invariant. This has many immediate consequences including the need to include the electric and magnetic fields associated with an electron in any description of the particle. Such dressing of charged particles in electromagnetism does not change the charge of the electron as photons are electrically neutral. For non-abelian interactions there is, however, a further subtlety: the charge of such theories is itself not gauge invariant, unless it is acting on gauge invariant states. We cannot associate colour with a quark field if we do not take its (colour charged) gluonic dressing into account.

This raises many questions: can we construct a gauge invariant description of a charged particle? How do we single out physically meaningful descriptions? A review of our approach to these fundamental problems can be found here.

Fully answering these questions is the focus of most of the work done in the Plymouth particle physics group. It can be seen that there is indeed a plethora of possible solutions in an abelian theory and that perturbative calculations can be used to interpret them and single out relevant ones. For the unbroken non-abelian theory of Quantum Chromodynamics, we have shown that there is a topological obstruction to constructing a gauge invariant description of a quark. This means that we cannot expect to observe free particles with colour charges in nature. A major part of the research of this group is devoted to quantifying this result.

David McMullan, October 1997 (dmcmullan at plymouth dot ac dot uk)