Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The tools of perturbative Quantum Field Theory are by now a standard part of the theoretical
physicist's arsenal. In this thesis we investigate the spectral method, an approach that uses tools from
the quantum theory of scattering to calculate the O(~) corrections to fields. Speci cally, we investigate
whether the approach can be extended to deal with two interacting scalar elds with a mass gap in
(1+1) dimensions. To achieve this we need to verify the analyticity of the appropriate Jost function.
All the machinery to do so is introduced during the course of the thesis. This includes the eld theoretic
formalism which describes such a system, and the derivation of a number of di erential equations
from which the density of states can be constructed. The numerical method is also outlined. Concrete
results are presented to verify that the approach reproduces known results. Arguments related to
Levinson's theorem are then presented that suggest that the Jost function is indeed analytic, with
some caveats. / AFRIKAANSE OPSOMMING: Die gereedskap van perturbatiewe Kwantumveld-teorie is teen di e tyd al `n standaard-deel van die
teoretiese sikus se werkskis. In hierdie tesis ondersoek ons die spektrale metode, `n benadering wat
gereedskap van die kwantumteorie van verstrooing gebruik om die O(~) korreksie van velde te bereken.
Ons ondersoek spesi ek of die metode uitgebrei kan word om toepaslik te wees in die geval van twee
wisselwerkende skalaarvelde met `n massa-gaping in (1+1) dimensies. Vir hierdie doel moet ons bepaal
of die toepaslike Jost-funksie analities is of nie. Al die masjinerie om dit te bepaal word deur die loop
van hierdie tesis ingevoer. Dit sluit in die veld-teorietiese formalisme wat so `n stelsel beskryf, en die
a
eiding van `n aantal di erensiaal vergelykings wat gebruik kan word om die digtheid van toestande
te konstrueer. Die numeriese metode word ook beskryf. Konkrete resultate wat bevestig dat die
metode die korrekte antwoorde in `n analities bekende geval weergee, word verskaf. Argumente wat
verband hou met Levinson se stelling word gebruik om te bevestig dat die Jost-funksie inderdaad
analities is, met sekere voorbehoude.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/95995 |
| Date | 12 1900 |
| Creators | Capraro, Martin Horst |
| Contributors | Weigel, Herbert, Stellenbosch University. Faculty of Science. Dept. of Physics. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 77 p. |
| Rights | Stellenbosch University |
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