  We study a one-dimensional model of radiative heat transfer for which the
effect of the electromag- netic field is only from the scalar potential and
thereby ignoring the vector potential contribution. This is a valid assumption
when the distances between objects are of the order of nanometers. Using Lorenz
gauge, the scalar field is quantized with the canonical quantization scheme,
giving rise to scalar photons. In the limit as the speed of light approaches
infinity, the theory reduces to a pure Coulomb interaction governed by the
Poisson equation. The model describes very well parallel plate capacitor
physics, where a new length scale related to its capacitance emerges. Shorter
than this length scale we see greater radiative heat transfer. This differs
markedly from the usual Rytov fluctuational electrodynamics theory in which the
enhancement is due to evanescent modes shorter than the thermal wavelengths.
Our theory may explain recent experiments where charge fluctuations instead of
current fluctuations play a dominant role in radiative heat transfer. Finally,
due to the asymmetric electron-bath couplings, thermal rectification effects
are also observed and reported.
