Third quantization of the electromagnetic field

Abstract

We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is quantized to produce a field operator. Since the electromagnetic field is already second quantized, this corresponds to a third quantization. This approach allows certain calculations in quantum optics to be performed in a straightforward way in the Heisenberg picture. Aside from being a useful computational tool, this approach allows an interesting generalization of quantum optics and quantum electrodynamics that could be tested experimentally.