A new perspective on Kaluza-Klein theory

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dc.contributor.advisorScholtz, Frederik G. en_ZA
dc.contributor.authorHoroto, Langaen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Physics.en_ZA
dc.date.accessioned2023-11-27T12:03:11Z
dc.date.accessioned2024-01-08T20:19:54Z
dc.date.available2023-11-27T12:03:11Z
dc.date.available2024-01-08T20:19:54Z
dc.date.issued2023-12
dc.descriptionThesis (MSc)--Stellenbosch University, 2023.en_ZA
dc.description.abstractENGLISH ABSTRACT: Kaluza-Klein theories are classical theories that unify fundamental forces by treating them as general relativity in more than four spacetime dimensions. The existing theories of this nature make predictions which are not consistent with experiments. In this work, we develop a variant of such theories which is free of all their shortcomings. We achieve this through introduction of a postulate regarding matter and curvature of spacetime which we utilize in con- structing the Lagrangian. The resulting Lagrangian is the simplest Lagrangian respecting all the symmetries of 4D gauge theories and naturally incorporates the Higgs mechanism. However; such a Lagrangian is at odds with the current interpretation of General Relativity. We show that it is this inconsistency of gauge theories and interpretation of general relativity that results in the incor- rect value of the cosmological constant computed from quantum theory. From the equations that follow it is clear that - contrary to the popular assumption- the Ricci flat higher dimensional spacetime can not result in the complete the- ory of fundamental forces. We construct the standard model and show that the minimum number of dimensions of spacetime encompassing all fundamental forces is 16 which is again at variance with other higher dimensional theories. We conclude by showing that the theory does not only results in unification of the fundamental forces but also that of bosons and fermions by demonstrating that spin is a consequence of isometries of spacetime in the same manner that charge is.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Kaluza-Klein-teorieë is klassieke teorieë wat fundamentele kragte verenig deur ‘n Algemene Relatiwistiese beskrywing in meer as vier ruimte-tyd dimensies. Die bestaande teorieë van hierdie aard maak voorspellings wat nie ooreenstem met eksperimente nie. In hierdie werk ontwikkel ons ’n variant van sulke teo- rieë wat vry is van hierdie tekortkominge. Ons bereik dit deur middel van ’n postulaat rakende die ekwivalensie van materie en kromming van ruimte-tyd wat ons in staat stel om die Lagrange funksie te konstrueer. Hierdie Lagrange funksie is die eenvoudigste funksie wat al die simmetrieë van 4-dimensionele ykteorieë respekteer en sluit die Higgs-meganisme op ‘n natuurlike wyse in. So Lagrange beskrywing is egter in stryd met die huidige interpretasie van Algemene Relatiwiteit. Ons toon aan dat dit hierdie inkonsekwentheid van ykteorieë en die interpretasie van algemene relatiwiteit is wat lei tot die in- korrekte kosmologiese konstante wat deur kwantumteorie bereken word. Uit die vergelykings wat volg is dit duidelik dat - in teenstelling met die algemene aanname - die Ricci plat hoër dimensionele ruimte-tyd nie kan lei tot die volle- dige teorie van fundamentele kragte nie. Ons konstrueer die standaard model en toon aan dat die minimum aantal dimensies van ruimte-tyd wat alle fun- damentele kragte insluit 16 is wat verskil van ander hoër dimensionele teorieë. Ons sluit af deur aan te toon dat die teorie nie net tot vereniging van die fundamentele kragte lei nie, maar ook dié van Bosone en Fermione deur te demonstreer dat spin die gevolg is van isometrieë van ruimte-tyd op dieselfde manier as wat lading is.af_ZA
dc.description.versionMastersen_ZA
dc.format.extentvii, 109 pagesen_ZA
dc.identifier.urihttps://scholar.sun.ac.za/handle/10019.1/129043
dc.language.isoen_ZAen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subject.lcshKaluza-Klein theoriesen_ZA
dc.subject.lcshRelativity (Physics)en_ZA
dc.subject.lcshSpace and time -- Mathematical modelsen_ZA
dc.subject.lcshLagrange equationsen_ZA
dc.subject.lcshGeneral relativity (Physics) -- Mathematical modelsen_ZA
dc.subject.lcshGauge fields (Physics) -- Measurementen_ZA
dc.subject.nameUCTDen_ZA
dc.titleA new perspective on Kaluza-Klein theoryen_ZA
dc.typeThesisen_ZA
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