master thesis
Nikiša Plešec (Author), Miha Nemevšek (Mentor), Lorenzo Ubaldi (Co-mentor)

Abstract

This thesis explores the false vacuum decay rate of a scalar field at one-loop order in two, three, and four dimensions using semiclassical methods. The results are compared with established analytical solutions in the thin-wall limit, where the true and false vacua are nearly degenerate. A central element of this work is the bounce solution, which describes the most probable tunneling path between the false and true vacua, along with its associated Euclidean action. The action is renormalized to eliminate divergences in even dimensions, and the renormalization group running is examined. The contribution of quantum fluctuations around the bounce solution, expressed as a ratio of functional determinants, is analyzed and determined using the Gel'fand-Yaglom theorem. As part of this approach, the zero eigenvalues are systematically removed. The ratio of functional determinants is renormalized, providing a finite result for the decay rate. This result is consistent with the thin-wall approximation and remains valid until the false vacuum transitions into an inflection point.

Keywords

false vacuum decay;decay rate;scalar field theory;thin-wall limit;quantum fluctuations;renormalization;functional determinant;

Data

Language: English
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [N. Plešec]
UDC: 530.145
COBISS: 208053507 Link will open in a new window
Views: 282
Downloads: 202
Average score: 0 (0 votes)
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Other data

Secondary language: Slovenian
Secondary title: Razpadna širina lažnega vakuuma skalarnega polja na eni zanki
Secondary abstract: Delo obravnava razpad lažnega vakuuma skalarnega polja na nivoju ene zanke v dveh, treh in štirih dimenzijah, z uporabo semiklasičnega približka. Vsi rezultati so primerjani z analitičnimi rešitvami v limiti tanke stene, kjer sta pravi in lažni vakuum skoraj degenerirana. Osrednji element dela je odskočna rešitev, ki opisuje najbolj verjetno pot tuneliranja med lažnim in pravim vakuumom, skupaj s pripadajočo Evklidsko akcijo. Za odstranitev divergenc v sodih dimenzijah je potrebno akcijo renormalizirati in obravnavati tekoče konstante v kontekstu renormalizacijske grupe. Prispevek kvantnih fluktuacij se v razpadni širini pojavi kot razmerje funkcionalnih determinant. Ta je izvrednoten z uporabo Gel'fand-Yaglomovega izreka, ki zahteva dodatno odstranitev ničelnih lastnih vrednosti. Razmerje determinant je renormalizirano in poda končno razpadno širino. Dobljeni rezultat se ujema z analitično rešitvijo v limiti tanke stene, veljaven pa je dokler lažni vakuum ne postane prevojna točka potenciala.
Secondary keywords: razpad lažnega vakuuma;razpadna širina;skalarna teorija polja;limita tanke stene;kvantne fluktuacije;renormalizacija;funkcionalna determinanta;
Type (COBISS): Master's thesis/paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za fiziko
Source comment: Prešernova nagrada študentom Fak. za matematiko in fiziko za l. 2024
Pages: 113 str.
ID: 25059913