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

[摘要] ENGLISH ABSTRACT: The tools of perturbative Quantum Field Theory are by now a standard part of the theoreticalphysicist's arsenal. In this thesis we investigate the spectral method, an approach that uses tools fromthe quantum theory of scattering to calculate the O(~) corrections to fields. Speci cally, we investigatewhether the approach can be extended to deal with two interacting scalarelds 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 theeld theoreticformalism which describes such a system, and the derivation of a number of di erential equationsfrom which the density of states can be constructed. The numerical method is also outlined. Concreteresults are presented to verify that the approach reproduces known results. Arguments related toLevinson's theorem are then presented that suggest that the Jost function is indeed analytic, withsome caveats.

[发布机构] Stellenbosch University