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Electromagnetic Duality in SO(3) Yang-Mills Theory: Bachelor Thesis
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Elektromagnetisk Dualitet i SO(3) Yang-Mills Teori : Kandidat Avhandling (Swedish)
Abstract [en]

We introduce the historical context and motivation for the search for magnetic monopoles or monopole-like objects. Beginning the theoretical part we investigate the properties of groups as they relate to symmetries in physical theories. Using this as a basis we investigate the requirements for global and local gauge invariance for a scalar field, the latter giving the non-trivial connection to a gauge field. From this we present the Georgi-Glashow model and develop its particle spectrum using the connected Higgs field and its associated Higgs mechanism. We then present the electromagnetic duality by extending the Maxwell's equations toinclude magnetic sources. Using the assumption of magnetic sources we present the Dirac quantization condition, motivating the quantization of electric charge. Returning to our model we present the 't Hooft-Polyakov ansatz and investigate its defining properties as a finite energy soliton in our Higgs field. We show the magnetic properties and motivate its validity as a monopole like object. Continuing we define BPS-states on the lower bound for the mass of a monopole like object with magnetic and electric charge. Giving a BPS monopole as a solution in the vein of 't Hooft and Polyakov. Returning to the electromagnetic duality we propose the Montonen-Olive conjecture by exchanging massive vector bosons in our model with the BPS monopoles we developed. We shortly comment on evident problems and present supersymmetry as a possible solution. Finally we present the Witten Effect by allowing a CP violating term in our Lagrangian. From this we extend the Montonen-Olive conjecture to include invariance under the SL(2,Z) group.

Place, publisher, year, edition, pages
2018. , p. 25
Series
FYSAST ; FYSKAND1083
Keywords [en]
Montonen-Olive conjecture, BPS states, 't Hooft-Polyakov monopole, Witten effect, SL(2, Z) invariance
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:uu:diva-354716OAI: oai:DiVA.org:uu-354716DiVA, id: diva2:1222380
Educational program
Bachelor Programme in Physics
Supervisors
Examiners
Available from: 2018-07-02 Created: 2018-06-21 Last updated: 2018-07-02Bibliographically approved

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Electromagnetic Duality - Jim Lundin(1321 kB)31 downloads
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