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Vacuum polarization energy for BPS solitons
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_ | 1867614112308002816 |
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| access_status_str | Open Access |
| author | Meyer, Willem Johannes |
| author2 | Weigel, H. |
| author_browse | Meyer, Willem Johannes Weigel, H. |
| author_facet | Weigel, H. Meyer, Willem Johannes |
| author_sort | Meyer, Willem Johannes |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2025. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/134703 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:46:51.765Z |
| 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:10019.1/134703 Vacuum polarization energy for BPS solitons Meyer, Willem Johannes Weigel, H. Muller-Nedebock, K. K. Stellenbosch University. Faculty of Science. Dept. of Physics. Vacuum polarization -- Mathematical models Solitons -- Mathematical models Energy levels (Quantum mechanics) Spectral theory (Mathematics) Scattering (Mathematics) UCTD Thesis (MSc)--Stellenbosch University, 2025. Meyer, W. J. 2025. Vacuum Polarization Energy for BPS Solitons. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/e872fb1f-7fdb-4295-b81c-24a7c936a8e6 ENGLISH ABSTRACT: The main objective of this thesis is to compute the first-order quantum correction to the classical energy, the Vacuum Polarization Energy (VPE), for Bogomol’nyi-Prasad-Sommerfield (BPS) solitons in D = 1 + 1 field theories. We will in vestigate a set of models with some variational parameter that effects the shape of the soliton but not the values of the soliton at the spatial infinities. We will show that the classical energy depends solely on the values of the soliton at the spatial infinities. Therefore, the classical energy is degenerate with respect to this parameter. In contrast, the VPE does depend on the shape of the soliton and will thus lift the degeneracy. We will use numerical spectral methods, involving scattering theory, to compute the VPE and determine the dependence of the VPE on the variational parameter. We will consider two different types of models: the first type is based on the ϕ⁴ model with a spatially dependent external impurity, while the second type involves two coupled scalar fields. The latter has the particular feature of possessing two distinct sets of vacua that we call primary and secondary. The soliton always approaches a primary vacuum at spatial infinity but may dwell in a secondary vacuum within an arbitrarily large, though finite, region of space. The VPE decreases with the size of this region without a lower bound. Hence, the soliton becomes unstable at this order of the semi-classical expansion. AFRIKAANSE OPSOMMING: Die hoofdoel van hierdie tesis is om die eerste-orde kwantumkorreksie tot die klassieke energie, die valuesakuum-polarisasie-energie (VPE), vir Bogomol’nyi-Prasad-Sommerfield (BPS) solitone in veldteorieë in D = 1 + 1 dimensies te bereken. Ons sal ’n stel modelle ondersoek met sommige variasionele parameters wat die vorm van die solitoon beïnvloed, maar nie die waardes van die solitoon by die ruimtelike oneindighede nie. Ons sal wys dat die klassieke energie slegs afhang van die waardes van die solitoon by die ruimtelike oneindighede. Daarom is die klassieke energie onafhanklik van hierdie parameter. Dit is egter nie die geval vir die VPE nie wat wel geaffekteer word deur die vorm van die solitoon en dus afhanklik is van die variasionele parameter. Ons sal numeriese spektraal metodes, wat verstrooiingsteorie insluit, gebruik om die VPE te bereken en die afhanklikheid van die VPE op die variasionele parameter te bepaal. Ons sal twee verskillende tipes modelle oorweeg: die eerste tipe is gebaseer op die ϕ⁴ model met ’n ruimtelik afhanklike eksterne onsuiwerheid, terwyl die tweede tipe twee gekoppel skalaar velde behels. Die laasgenoemde model het die besondere eienskap dat dit twee onderskeibare stelle vakuums besit, wat ons primêr en sekondêr noem. Die solitoon nader altyd ’n primêre vakuum by ruimtelike oneindigheid, maar kan wel in ’n sekondêre vakuum binne ’n arbitrêr groot, maar eindige, gebied verkeer. Die VPE neem af met die grootte van hierdie gebied sonder ’n onder grens. Dus word die solitoon onstabiel op hierdie orde van die semi-klassieke uitbreiding. Masters 2025-12-24T07:58:55Z 2025-12-24T07:58:55Z 2025-12 Thesis https://scholar.sun.ac.za/handle/10019.1/134703 en Stellenbosch University viii, 65 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Vacuum polarization -- Mathematical models Solitons -- Mathematical models Energy levels (Quantum mechanics) Spectral theory (Mathematics) Scattering (Mathematics) UCTD Meyer, Willem Johannes Vacuum polarization energy for BPS solitons |
| title | Vacuum polarization energy for BPS solitons |
| title_full | Vacuum polarization energy for BPS solitons |
| title_fullStr | Vacuum polarization energy for BPS solitons |
| title_full_unstemmed | Vacuum polarization energy for BPS solitons |
| title_short | Vacuum polarization energy for BPS solitons |
| title_sort | vacuum polarization energy for bps solitons |
| topic | Vacuum polarization -- Mathematical models Solitons -- Mathematical models Energy levels (Quantum mechanics) Spectral theory (Mathematics) Scattering (Mathematics) UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/134703 |
| work_keys_str_mv | AT meyerwillemjohannes vacuumpolarizationenergyforbpssolitons |