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arXiv 0709.1828hep-th
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类电背景下QED中的单圈能量动量张量

One-loop energy-momentum tensor in QED with electric-like background

S. P. Gavrilov, D. M. Gitman

摘要:

我们得到了类电背景下狄拉克场的平均能量动量张量和平均电流密度的非微扰单圈表达式。这种计算的目的之一是在这样的理论中给出一个一致的反作用描述。两种情况下的初始状态被认为是:真空状态和热平衡状态。首先,我们对真空初态进行计算。在得到的表达式中,我们分离的贡献,由于粒子产生和真空极化。后者的贡献与海森堡-欧拉拉格朗日量有关。然后,我们研究了热初态的情况。在这里,我们分离的贡献,由于粒子的创建,真空极化,和贡献,由于在初始状态的粒子的外部场的工作。所有这些贡献进行了详细研究,在不同的制度,弱和强的领域和低温和高温。所得到的结果使我们能够建立限制的电场和它的持续时间下,QED与一个强的恒定电场是一致的。在这样的限制下,可以忽略由电场产生的粒子的反反应。所得结果将Heisenberg-Euler的能量密度计算推广到任意强电场的情形。

英文摘要:

We have obtained nonperturbative one-loop expressions for the mean energy-momentum tensor and current density of Dirac's field on a constant electric-like background. One of the goals of this calculation is to give a consistent description of back-reaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to the Heisenberg-Euler Lagrangian. Then, we study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the back-reaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.

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