A transport equation for dipole radiation is derived from quantum electrodynamics. The radiation field is described in terms of a space–time Wigner function, which accounts for the position–momentum and time–energy Heisenberg uncertainty relations on an equal footing. The formalism involves the Heisenberg equations of motion for the quantized electric field and the polarization density. It is shown that the radiative transfer equation introduced phenomenologically in textbooks holds at the large spectral band limit, which is characteristic of a slowly varying radiation field in a medium with slowly varying emission and absorption coefficients.

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使用维格纳相空间形式主义推导线辐射的输运方程

偶极辐射的输运方程式是从量子电动力学得出的。用时空维格纳函数描述辐射场，该函数解释了在平等的基础上位置-动量和时间-能量-海森堡不确定性关系。形式主义涉及用于量化电场和极化密度的海森堡运动方程。结果表明，从现象学上引入教科书的辐射传递方程在较大的光谱带范围内成立，这是发射和吸收系数缓慢变化的介质中辐射场缓慢变化的特征。