Complications in Coulomb gauge QCD
In 1980, Christ and Lee wrote a paper titled 'Operator ordering and Feynman rules in gauge theories'. In this paper they showed that the Hamiltonian formulation of a non-abelian gauge theory in a general non-covariant gauge is complicated by problems of operator ordering, leading to new nonlocal interactions they call V1 + V2. In particular this applies to the familiar Coulomb gauge. More recently, Cheng and Tsai have arrived at the same ordering by careful attention to the fact that the Gauss-law constraint is not an operator equation. On the other hand, it is known that the naive Coulomb gauge Feynman rules in non-abelian gauge theory give rise to ambiguous integrals, in addition to the usual ultraviolet divergences. This thesis shows how these ambiguities can be resolved to all orders in perturbation theory. This is done by defining a gauge that interpolates smoothly between the Feynman gauge and the Coulomb gauge, and then using a diagrammatic method to combine the different contributions that arise. The extra terms V1 + V2 of Christ and Lee are then identified with certain two loop ambiguous terms. The only remaining question is whether the method of resolving the ambiguities is compatible with renormalisation. An investigation into the extra complications that renormalisation introduces is carried out.