Quantum electrodynamics near a dielectric half-space

Abstract

We determine the photon propagator in the presence of a non-dispersive dielectric half-space and use it to calculate the self-energy of an electron near a dielectric surface.

Quantum electrodynamics of a free particle near dispersive dielectric or conducting boundaries

“…This introduces the additional complication that the reflection coefficient has branch points at k z =±ik , causing the formulas (12) and (13) to become ambiguous. Our method is reliant on the fact that whatever happens above −ik in the lower half of the k z plane does not preclude a contour deformation that allows us to simply pick up the residue at k z =−ik .This inability to deform a contour once damping is introduced has been investigated in detail in [23], where it is concluded that standard derivations of the Lifshitz formula with damping must contain an unspecified inconsistency (a statement reflected by experimental results [24]).…”

“…However, one can use the Lifshitz theory and write the electromagnetic field as a response to fluctuating noise currents inside the material (see, for example, [18]). The Green's function describing this response involves the reflection coefficients of the surface so that one necessarily ends up with the same formulas (12) and (13), regardless of the specific choice of dielectric function. Proceeding along these lines, we use our formulas to investigate a model in which a restoring force is introduced [19], summarized by the introduction of a new characteristic frequency ω T into the dielectric function:…”

“…While the corresponding calculations of other quantities such as the magnetic moment shift [10] have more obvious experimental relevance, the mass shift calculation turns out to be technically simple, and gives exact results even for dispersive surfaces. Thus, we present the self-energy calculation as both an accessible example of our formulation of quantum field theory near boundaries, and as a clarification of a previous result [11,12].…”

“…[13]). But, when boundaries are present even one-loop calculations of quantum electrodynamics get very cumbersome [12]. Since we seek only the change in the self-energy that is attributable to the surface, we take a different, more appropriate approach.…”

Quantum electrodynamics of inhomogeneous anisotropic media

“…On the other hand, the present condition is also close to the generalized Coulomb gauge condition considered in Ref. [26]. For the case of non-dissipative and also non-dispersive isotropic media, i.e., for the case of constant dielectric permittivity, a close condition can be obtained.…”