Limits of the photon model in cavity QED and quantum optics

Summary form only given. The photon model of the quantum electromagnetic (EM) field has recently been developed further for the areas of cavity QED and quantum optics in dielectric media. The basic problem is that the natural EM field modes to use (Fox-Li modes) are eigenfunctions of a non-Hermitian operator, unlike the normal modes that satisfy a Helmholtz equation. Such eigenfunctions have complex eigenvalues, and unlike the situation for normal modes, orthogonality occurs with a related set of adjoint mode functions, satisfying eigenvalue equations involving the adjoint operator. The standard canonical quantization procedure based on expanding the vector potential in terms of modefunctions then runs into difficulties, and the desired outcome of showing the EM field is equivalent to a set of quantum harmonic oscillators (QHO) is hard to achieve, as this paper shows.