Third quantization of the electromagnetic field

TL;DR

This paper introduces a third quantization framework for the electromagnetic field, enabling new quantum optics calculations and generalizations of quantum electrodynamics, with potential experimental tests via photon scattering.

Contribution

It proposes a novel third quantization approach for the electromagnetic field, extending quantum optics and QED beyond conventional second quantization.

Findings

Enables quantum optics calculations in the Heisenberg picture.

Provides a generalized quantum electrodynamics framework.

Suggests experimental tests through photon scattering.

Abstract

We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. 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 Schrodinger 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.