ABSTRACT
The second quantization of the electromagnetic field in quantum electrodynamics is generally achieved by starting with a finite volume in which the field can appear in a discrete, although infinite, set of modes. The introduction of canonical variables casts the Hamiltonian into a form similar to that for the harmonic oscillator, which can easily be quantized by imposing canonical commutation relations. Finally, the customary continuous spectrum ensues when the volume is increased to infinity. For a long time, this continuous and unlimited spectrum of the electromagnetic field has been considered exclusively. To obtain solutions for actual physical problems, the formalism of quantum field theory together, with all its conjurings to overcome divergences, had to be developed. The question of modification of atomic properties in the presence of conducting walls has gained considerable interest. Introducing conductors into a physical system imposes boundary conditions on the electromagnetic field and leads back to a discrete spectrum in the case of a finite volume enclosed in a cavity. In the following sections, we discuss the consequences of those boundary conditions on the properties of atoms enclosed in a cavity, summarized under the term “cavity quantum electrodynamics.”
