Magnetic Oscillations and Maxwell Theory

We explore the possibility of using the Kaluza-Klein geometry of Riemannian Submersions to modify the classical Maxwell Theory. We further argue that the resulting modification of Electromagnetism— cf. equations (3) as well as (4) and (5)—may be interesting in the context of, among other topics, magnetic oscillations in metals. 1. The Maxwell equations are geometric and can be expressed as equations defining a principal U(1) connection. Such a connection A is a differential 1-form on the total space of a U(1)-bundle, which in addition satisfies R∗ θA = 0, A( ∂ ∂θ ) = 1. (1) Here θ ∈ U(1), Rθ denotes the U(1)-action on the bundle and ∂ ∂θ is the canonical vertical vector field induced by this action. Now if FA = dA is the curvature, then (in the absence of nonstatic charge distributions) the Maxwell equations become dFA = 0, d ∗(fFA) = 0, (2) where f is the so called material constant (like the dielectric constant, the inverse of the magnetic permeability, etc.) 1 In what follows all physical constants irrelevant for our discussion are set to 1.