We consider an approach in which the usual wave function ${\psi }_j\left(x_j\right)$ in the quadrature representation of mode $j$ of the electromagnetic field is further quantized to produce a field operator ${\widehat{\psi }}_j\left(x_j\right).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schrödinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.

• Received 21 October 2020
• Revised 20 August 2021
• Accepted 24 September 2021

DOI:https://doi.org/10.1103/PhysRevA.104.063702