In this paper, we calculate tree-level currents of created particles in strong background electric fields in 4D QED for various initial states. Namely, we do that in pulse background for initial vacuum and thermal states at past infinity. In both cases, we find that the current grows linearly with the length of the pulse with coefficients of proportionality containing the characteristic Schwinger’s factor. For the constant electric field background, we calculate the current for several different initial states. We observe that in such a case the current is either zero or linearly divergent. We explain the reason for such a behavior and compare the situation in ordinary and scalar QED. Finally, we calculate the current in two-dimensional situation in the presence of such settings when the so-called Klein paradox can be observed.

中文翻译：

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强电场中生成对的电流

在本文中，我们计算了 4D QED 中强背景电场中创建粒子在各种初始状态下的树级电流。即，我们在脉冲背景下对过去无穷大的初始真空和热状态进行此操作。在这两种情况下，我们发现电流随着脉冲长度线性增长，比例系数包含特征施温格因子。对于恒定电场背景，我们计算了几种不同初始状态的电流。我们观察到，在这种情况下，电流要么为零，要么呈线性发散。我们解释了这种行为的原因，并比较了普通 QED 和标量 QED 中的情况。最后，当可以观察到所谓的克莱因悖论时，我们在存在这种设置的情况下计算二维情况下的电流。