Anomalous magnetic moment of an electron near a dispersive surface

Abstract: Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a non-dispersive dielectric and an undamped plasma, but the electron is described by the Dirac equation without matter-field quantization. Perturbation theory in the Dirac equation leads to a general formula for the magnetic moment shift in terms of integrals over products of electromagnetic mode functions. In each of the models investigated contour integration techniques over a complex wave vector can be used to derive a general formula featuring just integrals over transverse electric and transverse magnetic reflection coefficients of the surface. Analysis of the magnetic moment shift for several classes of materials yields markedly different results from the previously considered simplistic 'perfect reflector' model, due to the inclusion of physically important features of the electromagnetic response of the surface such as evanescent field modes and dispersion in the material. For a general dispersive dielectric surface, the magnetic moment shift of a nearby electron can exceed the previous prediction of the perfect-reflector model by several orders of magnitude.