A model for U(1) gauge theories over a compact Lie group is described usingR×S 3 as background space. A comparison with other results is given. Electrodynamics equations are obtained. Finally, some considerations and observations about gravity onR×S 3 space are presented.

The solution of the Klein-Gordon equation for a complex scalar field in the presence of an electrostatic field orthogonal to a magnetostatic field is analyzed. Considerations concerning the quantum Hall-type evolution are presented also. Using the Hamiltonian with a self-interaction term, we obtain a critical value for the magnetic field in the case of the spontaneous symmetry breaking.