Symmetries of the boundary theorem in electrodynamics and beyond
Kristján Óttar Klausen - University of Iceland
Symmetries of Maxwell's equations of electrodynamics are studied from the point of view of Stokes' boundary theorem in geometric calculus. We show how the magnetic vector potential has richer symmetry and elaborate on it's topological properties using hydrodynamical analogies. Stokes' theorem for bivector fields is then considered and it's relation to Yang-Mills theory and SU(2) gauge potentials discussed. We conclude by briefly reviewing effective gauge theory for spin dynamics.