Synchrotron radiation was originally studied by classical methods using the Liénard–Wiechert potentials of electric currents. Subsequently, quantum corrections to the classical formulas were studied, considering the emission of photons arising from electronic transitions between spectral levels, described in terms of the Dirac equation. In this paper, an intermediate approach is considered, in which electric currents generating the radiation are considered classically while the quantum nature of the radiation is taken into account exactly. Such an approximate approach may be helpful in some cases; it allows one to study one‐photon and multi‐photon radiation without complicating calculations using corresponding solutions of the Dirac equation. Here, exact quantum states of an electromagnetic field interacting with classical currents are constructed and their properties studied. With their help, the probability of photon emission by classical currents is calculated and relatively simple formulas for one‐photon and multi‐photon radiation are obtained. Using the specific circular electric current, the corresponding synchrotron radiation is calculated. The relationship between the obtained results and those known before are discussed, for example with the Schott formula, with Schwinger calculations, with one‐photon radiation of scalar particles due to transitions between Landau levels, and with some previous results of calculating two‐photon synchrotron radiation.

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电磁场与经典电流相互作用的量子态及其在辐射问题中的应用

同步辐射最初是使用电流的Liénard-Wiechert势通过经典方法研究的。随后，研究了对经典公式的量子校正，考虑了由狄拉克方程描述的，由光谱能级之间的电子跃迁引起的光子发射。在本文中，考虑了一种中间方法，其中经典地考虑了产生辐射的电流，同时准确地考虑了辐射的量子性质。这种近似方法在某些情况下可能会有所帮助；它允许人们研究单光子和多光子辐射，而无需使用狄拉克方程的相应解来使计算复杂化。这里，构造了与经典电流相互作用的电磁场的精确量子态，并研究了它们的性质。在他们的帮助下，可以计算出经典电流发出光子的概率，并获得了单光子和多光子辐射的相对简单的公式。使用特定的圆形电流，计算相应的同步辐射。讨论了所得结果与以前已知结果之间的关系，例如，使用了Schott公式，Schwinger计算，由于Landau能级之间的跃迁而导致了标量粒子的单光子辐射以及计算双光子同步加速器的一些先前结果。辐射。计算了经典电流发射光子的概率，并获得了单光子和多光子辐射的相对简单公式。使用特定的圆形电流，计算相应的同步辐射。讨论了所得结果与以前已知结果之间的关系，例如，使用了Schott公式，Schwinger计算，由于Landau能级之间的跃迁导致了标量粒子的单光子辐射以及计算双光子同步加速器的一些先前结果。辐射。计算了经典电流发射光子的概率，并获得了单光子和多光子辐射的相对简单公式。使用特定的圆形电流，计算相应的同步辐射。讨论了所得结果与以前已知结果之间的关系，例如，使用了Schott公式，Schwinger计算，由于Landau能级之间的跃迁而导致了标量粒子的单光子辐射以及计算双光子同步加速器的一些先前结果。辐射。