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Higher-Form Symmetries and their Spontaneous Breaking

Berzan, Nichita (2023) Higher-Form Symmetries and their Spontaneous Breaking. Bachelor's Thesis, Physics.


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In this thesis we review aspects of higher-form symmetries by primarily studying the free U(1) gauge theory and its one-form symmetries. At first we discuss differential forms and some necessary aspects of differential geometry. We continue by examining different formulations of Maxwell's theory, derive the equations of motion in the differential form notation, and touch on the topic of electromagnetic duality. We proceed by formulation the usual notion of ordinary symmetries in terms of operators and extending this notion to higher-form symmetries by considering higher dimensional charged objects and currents. Finally, we review essential topics related to spontaneous symmetry breaking and conclude that the photon can be viewed as the Goldstone boson of a spontaneously broken one-form symmetry of Maxwell's theory.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Boer, D.
Degree programme: Physics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 19 Jul 2023 08:33
Last Modified: 19 Jul 2023 08:33

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