Electromagnetic field stress tensor between dielectric half -spaces

The stress tensor for the quantized electromagnetic field is calculated in the region between a pair of dispersive, dielectric half-spaces. This generalizes the stress tensor for the Casimir energy to the case where the boundaries have finite reflectivity. Of particular inter est is the sign and magnitude of the energy density of the electromagnetic field compared to Minkowski vacuum. We find that the energy density is described by two terms: a negative position-independent (Casimir) term, and a positive position-dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region. We also include the effects of finite temperature. This allows us to discuss the circumstances under which the weak energy condition and the null energy condition can be violated in the presence of finite reflectivity and finite temperature. This is of interest, since the failure in the classical energy conditions may allow for some bizarre effects in gravity theory, such as constructing traversable wormholes.;Another point of interest is the behavior of mean squared fields and the energy density near the interface that separates the vacuum region from the dielectric half-space. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. This divergence is not considered to be physical, but as resulting from imposing unrealistic boundary conditions on the electromagnetic field.;Finally, the possibility of repulsive Casimir forces between small metal spheres and a dielectric half-space is discussed. We treat a model in which the spheres have a dielectric function given by the Drude model, and the radius of the sphere is small compared to the corresponding plasma wavelength. The half-space is also described by the same model, but with a different plasma frequency. We find that in the retarded limit, the force is quasi-oscillatory. This leads to the prediction of stable equilibrium points at which the sphere could levitate in the Earth's gravitational field. This seems to lead to the possibility of an experimental test of the model. Comments are given about the effects of the plasmon modes in the sphere on the force. The effects of finite temperature on the force are also studied, and found to be rather small at room temperature. However, thermally activated transitions between equilibrium points could be significant at room temperature.