The structure of quantum chromodynamics at the symmetric point

This thesis contains a study on the structure of the vertex functions of Quantum Chromodynamics (QCD) in both linear and non-linear gauges. In particular we show results for the arbitrary linear covariant gauge at two loops as well as renor- malizing the one loop non-linear Curci-Ferrari gauge and maximal abelian gauge (MAG). The full minimal subtraction MS and momentum subtraction (MOM) scheme renormalization of QCD is performed in all three gauges. This is carried out for an arbitrary colour group at one loop for the maximal abelian gauge and at two loops for the arbitrary linear covariant and Curci-Ferrari gauges. From the n loop MS results the (n + 1) loop β-functions and anomalous dimensions can be constructed in the respective gauges for each MOM scheme. This is demonstrated in all of the gauges considered. In addition to analysing the vertex functions at the symmetric subtraction point for both the MS and MOM schemes, we also consider an operator insertion into the quark 2-point function at the asymmetric point with an interpolating parameter. This requires a new configuration setup and introduces new master integrals which we determine. The scalar, vector and tensor operators are considered along with W2 and ∂W2, the twist-2 Wil- son operators for moment n = 2. The operator renormalization is performed at two loops in the MS and modified regularization invariant (RI′) scheme, both of which are preferred schemes of the lattice. Following the construction of the conversion function for the scalar operator for checking purposes, the amplitudes are presented for all other operators in the MS scheme.