Vacuum-to-vacuum transition probability and radiation in a medium

• Quantum viewpoint of radiation in a medium based on the vacuum-to-vacuum transition probabilities.
• Mathematical method in handling radiation in a medium for arbitrary sources.
• Radiated energy and power for arbitrary current distributions in a medium.
• Explicit power of radiation in a medium in a bounded region.

We recast the vacuum-to-vacuum transition probability for the description of radiation in an isotropic medium of permeability μ, and permittivity ε, in a form which brings us in contact with radiation theory in vacuum. Using the inherited property of such a system, with arbitrary current distributions, of emitting photons via the Poisson distribution, the average number of photons emitted in such a medium is directly obtained from which the power of radiation is readily extracted. As an application, the power of radiation, emitted by a charged particle, in a medium trapped between perfectly conducting neutral parallel plates for arbitrary finite separations is explicitly obtained.