University of Twente Student Theses
A classical treatment of scalar electrodynamics : Gauge theory in the Port-Hamiltonian framework
Grimbergen, Jeroen (2020) A classical treatment of scalar electrodynamics : Gauge theory in the Port-Hamiltonian framework.
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| Abstract: | The charged, massive Klein-Gordon field is a scalar field with a global U(1)-gauge symmetry. It is coupled to the Maxwellian electromagnetic field to get a system that has a local U(1)-gauge symmetry. We study the classical field theory of the Klein- Gordon field coupled to the electromagnetic field on a curved spacetime. The spacetime is foliated into spacelike hypersurfaces, each corresponding to a single “time”, such that a Hamiltonian theory may be formulated. Hamilton’s equations of motion and the gauge symmetries are worked out for the Klein-Gordon-Maxwell system under the assumption that the total energy of the system is constant. Port-Hamiltonian theory is used to reformulate the dynamics in a way that allows for the treatment of energy exchange with the environment. In the port-Hamiltonian formulation, however, the gauge symmetries are obscured. |
| Item Type: | Essay (Bachelor) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics, 33 physics |
| Programme: | Applied Mathematics BSc (56965) |
| Link to this item: | https://purl.utwente.nl/essays/81888 |
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