Quark confinement in quantum chromodynamics

Abstract

Modern theories of elementary particles are based on principles such as symmetry and simplicity. This does not mean that it is always easy to extract predictions from them concerning phenomena. An example that is this subject of this thesis is the problem of confinement in quantum chromodynamics: It is not clear whether this theory contains a dynamical mechanism preventing the emergence of its fundamental constituents (the quarks and gluons) as free particles. In addition there is the intimately related problem of why only certain types of bound states seem to be producable in this theory. The first chaper introduces quantum chromodynamics and confinement. It is after a discussion of attempts to prove various pans of the confinement problem that the scope of this present investigation is defined, it will be confined to the question concerning the non production of quarks in quantum chromodynamics. After a chapter discussing some relevant mathematical and physical features of quantum chromodynamics the remainder of the thesis is devoted to developing and presenting a proof of quark confinement. Some interesting (and in some cases only recently understood) results in field theory emerge along the way concerning the so-called axial gauges.