We show how to evaluate divergent asymptotic series using a modified Borei resummation method. We develop and test this technique using three different perturbative expansions of the anharmonic oscillator. In the first two expansions this provides the energy eigenvalues directly; however, in the third method we tune the wavefunctions to achieve the correct large X behaviour, as first illustrated in 1. This tuning technique allows us to determine the energy eigenvalues up to an arbitrary level of accuracy with remarkable efficiency. We give numerical evidence to explain this behaviour. We also refine the modified Borei summation technique to improve its accuracy. The main sources of error are investigated with reasonable error corrections calculated. Having developed a suitable resummation technique we show how to generate a type of local expansion for vacuum, one-and two-particle states in the Schrödinger representation of quantum field theory. We also develop a large distance expansion of the ร matrix in terms of a momentum cut-off. Computer programs capable of producing the local expansions of the wavefunctionals and S matrix to an arbitrary order are generated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:694792 |
| Date | January 2007 |
| Creators | Leonard, David |
| Publisher | Durham University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.dur.ac.uk/3930/ |
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