This thesis investigates various aspects of the relation between the lattice and continuum formulations of quantum field theories, in particular QCD. The aim of this is to gain a better insight into the theory of QCD, and to be able to relate more accurately the numbers obtained from lattice simulations to experimental values for physical quantities. The first part of this thesis (chapters 1 and 2) gives a general introduction to quantum field theory, with emphasis on the lattice formulation of QCD. The first chapter describes the functional integral formulation of gauge theories and how it can be used to study these theories non-perturbatively by discretising the space-time variables. The second chapter discusses the principles behind the renormalisation of these theories. The Ward and Slavnov-Taylor identities that are preserved non-perturbatively, and can be invoked when renormalising the theory, are derived. The final part of this chapter discusses the renormalisation of composite operators, using both perturbative and non-perturbative methods. In particular, it is shown how the chiral Ward identities can be used to extract renormalisation constants for the axial and vector currents and the ratio of the scalar to the pseudoscalar density. In chapter 3, results for <I>Z<SUB>A</SUB>, Z<SUB>V</SUB> </I>and <I>Z<SUB>P</SUB>/Z<SUB>s</SUB> </I>at β = 6.2 are presented and their effects on calculations of physical quantities like decay constants are discussed. The final chapter investigates the quark-gluon vertex. The form factors of the off-shell vertex function, and the symmetries and Slavnov-Taylor identities that may be used to reduce these form factors, are discussed. I then outline a method for extracting the running coupling from the vertex function. This also includes a discussion of the quark and gluon field renormalisation.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:662017 |
| Date | January 1996 |
| Creators | Skullerud, Jon Ivar |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/12965 |
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