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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:http://purl.utwente.nl/essays/81888
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