Local Varying-Alpha Theories
  In a recent paper we demonstrated how the simplest model for varying alpha
may be interpreted as the effect of a dielectric material, generalized to be
consistent with Lorentz invariance. Unlike normal dielectrics, such a medium
cannot change the speed of light, and its dynamics obey a Klein-Gordon
equation. This work immediately suggests an extension of the standard theory,
even if we require compliance with Lorentz invariance. Instead of a wave
equation, the dynamics may satisfy a local algebraic relation involving the
permittivity and the properties of the electromagnetic field, in analogy with
more conventional dielectric (but still preserving Lorentz invariance). We
develop the formalism for such theories and investigate some phenomenological
implications. The problem of the divergence of the classical self-energy can be
solved, or at least softened, in this framework. Some interesting new
cosmological solutions for the very early universe are found, including the
possibility of a bounce, inflation and expansion with a loitering phase, all of
which are induced by early variations in alpha.
