Vacuum polarisation energies of two interacting scalar fields with a mass gap in (1 + 1) dimensions

Capraro, Martin Horst (2014-12)

Thesis (MSc)--Stellenbosch University, 2014.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/95995
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