Quantum corrections to the kink-antikink potential

Lee, Zander (2017-03)

Thesis (MSc)--Stellenbosch University, 2017

Thesis

ENGLISH ABSTRACT : In quantum field theory vacuum polarization effects may drastically alter the classical properties of non-perturbative field configurations. This is especially the case when comparing the vacuum polarization energy (VPE) of configurations with different topological sectors which correspond to different particle numbers. For this reason we calculate the one-loop quantum correction to the kink-antikink potential by computing the VPE as a function of the kink-antikink separation. Being a quantum field theory calculation a proper renormalization must be applied. We compute the VPE by utilizing the spectral method which makes use of scattering data for fluctuations around the static kink-antikink configuration. In a first step we compare our numerical results for the kink background in the φ 4 and sine-Gordon models to analytical results from literature. In the next step the VPE is computed for backgrounds that have a kink and an antikink at a certain separation. Above a certain separation an unstable mode appears in the bound state spectrum of the symmetric channel. This unstable mode arises due to fluctuations which correspond to the variation of the separation distance. We exclude these fluctuations, because each calculation must be performed at a fixed separation. This enforces an orthogonality constraint in the symmetric channel. Ultimately, the O(~) quantum correction to the kink-antikink potential is extracted from the calculation of the VPE.

AFRIKAANSE OPSOMMING : In kwantumveldteorie kan die klassieke eienskappe van nie-perturbatiewe konfigurasies drasties verander word deur vakuum-polarisasie effekte. Hierdie is veral die geval wanneer die vakuum-polarisasie energie (VPE) van konfigurasies met verskillende topologiese sektore, wat ooreenstem met verskillende deeltjie nommers, vergelyk word. Vir hierdie rede bereken ons die een-lus kwantumkorreksie aan die kink-antikink potensiaal deur die VPE te bereken as ‘n funksie van die kink-antikink skeiding. ‘n Behoorlike hernormaliseering moet toegepas word omdat die ‘n veldteorie berekening is. Ons bereken die VPE deur gebruik te maak van die spektrale metode, wat gebruik maak van spreidingsdata vir fluktuasies rondom die statiese kink-antikink konfigurasie. In ‘n eerste stap vergelyk ons ons numeriese resultate vir die kink agtergrond in die φ 4 en sine-Gordon modelle met analitiese resultate van literatuur. In die volgende stap word die VPE bereken vir agtergronde wat ‘n kink en ‘n antikink het op ‘n sekere skeiding. Bo ‘n sekere skeiding verskyn ‘n onstabiele modus in die gebondetoestand spektrum van die simmetriese kanaal. Die onstabiele modus ontstaan as gevolg van fluktuasies wat ooreenstem met die variasie van die skeidingsafstand. Hierdie fluktuasies word uitgesluit omdat elke berekening gedoen moet word teen ‘n vaste skeiding. Hierdie dwing ‘n ortogonaliteit beperking in die simmetriese kanaal. Uiteindelik word die O(~) kwantumkorreksie aan die kink-antikink potensiaal uit die berekening van die VPE gehaal.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/100796
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