Quantum field theory methods

The research thesis will focus on the application of quantum field theory methods to various problems of interest in Theoretical Physics. In general this will involve computing relevant Green's functions by valuating Feynman diagrams to several loop orders. The main initial problem is to focus on the off-shell matrix elements that are relevant to higher moments of quark bilinear operators associated with the spin of the partons constituting hadrons and mesons such as the proton. The first phase will concern the flavour singlet unpolarized quark and gluon operators which will require an understanding of the ghost operators deriving from the linear covariant gauge fixing. The subsequent stage is to extend to the polarized case. As a parallel development similar operators will be studied in relation to the infrared properties of the gluon propagator which will involve the inclusion of mass. Knowledge of the structure of the operator anomalous dimensions is also relevant for more formal applications to conformal symmetry in quantum field theories especially that surrounding the energy-momentum tensor. The quantum structure associated with that operator will derive from the operator moment computations.

Central to the studies will be the use of computer algebra techniques as well as automatic Feynman diagram computations. The initial training with regard to this will be at a simple external momentum configuration. This is also necessary in order to cross-check operator mixing issues and consolidate our
understanding of the formalism from a second point of view.