We consider the question of the existence of an interacting continuum limit of Quantum Electrodynamics (QED). After a mention of why this limit may not exist and a discussion of how to formulate QED on a spacetime lattice we review the recent analytic and numerical work on the strong-coupling phase of QED. We take the view that there definitely exists a strong-coupling fixed point in the space of bare parameters but that the behaviour of renormalised quantities in its neighbourhood is not yet understood. For non-compact lattice QED with staggered fermions we develop an expansion in the inverse bare fermion mass that we use to calculate charge and fermion mass renormalisation. We evalute the vacuum polarisation to sixth order and present Feynman rules that allow its evaluation to higher orders. We also calculate the mass of the lowest lying pseudoscalar bound state and the chiral condensate. These physical quantities enable us to construct renormalisation group flow for all values of the bare charge. The expansion is checked against lattice perturbation theory and leads to a systematically improvable bound on the renormalised charge at the new fixed point. We also discuss compact QED coupled to scalars and find a chiral symmetry breaking transition at a non-zero value of the scalar coupling by using mean field theory. After establishing that this transition has Landau exponents we attempt to develop corrections to mean field theory by introducing fluctuations. The conclusion discusses the future of the large-mass expansion and lists some unresolved issues in lattice QED.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:649263 |
| Date | January 1990 |
| Creators | De Souza, Stephen William |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/14759 |
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