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.

中文翻译：

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电磁场的第三次量化

我们考虑一种方法，其中通常的波函数 ${\psi }_j\left(X_j\right)$ 在模式的正交表示中 $j$ 电磁场的进一步量化以产生场算子 ${\widehat{\psi }}_j\left(X_j\right).$由于电磁场已经被二次量化，这对应于附加或第三次量化。第三量化方法可用于在海森堡图像中执行某些量子光学计算，而这些计算只能在使用传统二次量化理论时在薛定谔图像中进行。这种方法还允许对量子光学和量子电动力学进行有趣的推广，类似于基本粒子理论中的对称破缺。可以使用提议的光子散射实验来测试广义理论的预测。