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Vacuum polarization energy of proca solitons in (1+1) dimensions
Thesis (MSc)--Stellenbosch University, 2025.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613782205792256 |
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| access_status_str | Open Access |
| author | Petersen, Damian Alvin |
| author2 | Weigel, Herbert
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| author_browse | Petersen, Damian Alvin Weigel, Herbert |
| author_facet | Weigel, Herbert
Petersen, Damian Alvin |
| author_sort | Petersen, Damian Alvin |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2025. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/132515 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:41:36.774Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/132515 Vacuum polarization energy of proca solitons in (1+1) dimensions Petersen, Damian Alvin Weigel, Herbert Stellenbosch University. Faculty of Science. Dept. of Physics. Vacuum polarization Solitons -- Mathematical models Scattering (Mathematics) Quantum field theory -- Data processing Scalar field theory Mathematical physics -- Data processing UCTD Thesis (MSc)--Stellenbosch University, 2025. Petersen, D. A. 2025. Vacuum Polarization Energy of Proca Solitons in (1+1) Dimensions. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/21302c91-c376-42fc-906c-5f5711c1e643 ENGLISH ABSTRACT: We calculate the leading quantum correction to the energies of localized, static field configurations known as solitons. This energy is called the vacuum polarization energy (VPE) and is extracted from scattering data of the quantum fluctuations about the soliton background. Taking advantage of the analytic properties of scattering data simplifies the final expression for the VPE to just an integral over the imaginary momentum in the scattering problem. This simplification may be challenged when additional seemingly non-analytic elements enter the problem. Here we investigate two such candidates in models defined in one space and one time dimension. First, in models with a relativistic dispersion and fields with different mass parameters, there is a non-analytic relation between the momenta that characterize the asymptotic states. Previously a method that solely employs the imaginary momentum was suggested. We show that the very same result is obtained with the real momentum formalism. Here the main obstacle that we solve is to avoid the Born approximation that is crucial for renormalization, but ill-defined for momenta with energies within the mass gap. Second, we consider the Proca model in which a scalar field interacts with a massive vector field (not a gauge field). In that model, the non-dynamical temporal component of the fluctuations is eliminated at the expense of a non-analytic normalization of the longitudinal component. We will show that the very same wave function normalization is required to obtain a Hermitian potential matrix for coupled scalar-Proca fluctuation scattering. In the numerical simulation, we will first construct the soliton and then verify that the real and imaginary formulations yield consistent results for the VPE of the Proca model. We also consider different masses for the scalar and Proca fields. Finally, we will discuss the dependencies on the model parameters of both the classical energy and its leading quantum correction. AFRIKAANSE OPSOMMING: Ons bereken die leidende kwantumkorreksie tot die energieë van gelokaliseerde, statiese veldkonfigurasies wat as solitons bekendstaan. Hierdie energie word die vakuumpolariser- ingsenergie (VPE) genoem en word onttrek vanuit die strooiingsdata van die kwantumfluk- tuasies rondom die solitonagtergrond. Deur gebruik te maak van die analitiese eienskappe van die strooiingsdata, word die finale uitdrukking vir die VPE vereenvoudig tot net ’n integraal oor die imaginˆere momentum in die strooiingsprobleem. Hierdie vereenvoudiging kan bevraagteken word wanneer bykomende, blykbaar nie-analitiese elemente in die prob- leem intree. Hier ondersoek ons twee sulke kandidate in modelle wat gedefinieer word in een ruimtelike- en een tydsdimensie. Eerstens, in modelle met ’n relativistiese disperger- ing en velde met verskillende massa parameters, bestaan daar ’n nie-analitiese verhouding tussen die momenta wat die asimptotiese state kenmerk. Voorheen is ’n metode voorgestel wat uitsluitlik van die imaginˆere momentum gebruik maak. Ons wys dat dieselfde resultaat bereik word met die reële momentum-formalisme. Die belangrikste belemmering wat ons oorkom, is om die Born-benadering te vermy wat van kardinale belang is vir hernormaliser- ing, maar swak gedefinieer is vir momenta met energieë binne die massagaping. Tweedens, oorweeg ons die Proca-model waarin ’n skalare veld met ’n massiewe vektorfeld (nie ’n eik- veld nie) in wisselwerking tree. In daardie model word die nie-dinamiese tydskomponent van die fluktuasies uitgeskakel ten koste van ’n nie-analitiese normalisering van die longit- udinale komponent. Ons sal wys dat dieselfde golffunksienormalisering vereis word om ’n Hermitiese potensiaalmatriks vir gekoppelde skalaar-Proca fluktuasie strooiing te verkry. In die numeriese simulasie sal ons eers die soliton konstrueer en dan verifieer dat die reële en imaginˆere formulerings ooreenstemmende resultate vir die VPE van die Proca-model oplewer. Ons oorweeg ook verskillende massas vir die skalaar- en Proca-velde. Laastens sal ons die afhanklikhede op die modelparameters van beide die klassieke energie en sy leidende kwantumkorreksie bespreek. Masters 2025-06-10T10:31:24Z 2025-06-10T10:31:24Z 2025-03 Thesis https://scholar.sun.ac.za/handle/10019.1/132515 en Stellenbosch University x, 77 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Vacuum polarization Solitons -- Mathematical models Scattering (Mathematics) Quantum field theory -- Data processing Scalar field theory Mathematical physics -- Data processing UCTD Petersen, Damian Alvin Vacuum polarization energy of proca solitons in (1+1) dimensions |
| title | Vacuum polarization energy of proca solitons in (1+1) dimensions |
| title_full | Vacuum polarization energy of proca solitons in (1+1) dimensions |
| title_fullStr | Vacuum polarization energy of proca solitons in (1+1) dimensions |
| title_full_unstemmed | Vacuum polarization energy of proca solitons in (1+1) dimensions |
| title_short | Vacuum polarization energy of proca solitons in (1+1) dimensions |
| title_sort | vacuum polarization energy of proca solitons in 1 1 dimensions |
| topic | Vacuum polarization Solitons -- Mathematical models Scattering (Mathematics) Quantum field theory -- Data processing Scalar field theory Mathematical physics -- Data processing UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/132515 |
| work_keys_str_mv | AT petersendamianalvin vacuumpolarizationenergyofprocasolitonsin11dimensions |