Transition amplitudes of interacting charged particles in an electric field and the Unruh effect
Transition amplitudes of interacting charged particles in an electric field and the Unruh effect
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电场中相互作用的带电粒子的跃迁幅度和安鲁效应
DOI：
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发表时间：
1997
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通讯作者：
R. Ruffini
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作者：
Claude Gabriel;Ph. Spindel;Serge Massar;R. Parentani;T. Piran;R. Ruffini
我们计算质量为 $M$ 和 $m$ 的带电粒子之间的跃迁幅度，这些粒子由恒定电场加速并通过第三个场的量子交换相互作用。我们进行第二量子化，以便考虑跃迁引起的反冲效应和带电场的真空不稳定性。尽管存在这两种效应，当交换的粒子为中性时，总体的平衡比仅为 $\mathrm{exp}[\ensuremath{\pi}{(M}^{2}\ensuremath{-}{m}^{2})/eE]。$ 因此，在极限 $(M\ensuremath{-}m)/\stackrel{\ensuremath{\rightarrow}}{M}0 下，$ 1 恢复了 Unruh 的结果以温度 $a/2\ensuremath{\pi}$ 为特征，其中 $a$ 是加速度。当交换的粒子带电时，其真空不稳定性阻碍了平衡状态的简单描述。然而，在交换粒子的电荷趋于零的极限下，平衡分布再次是玻尔兹曼分布，但其特征不仅在于温度，而且还在于交换粒子感受到的电势。因此，这项工作证实了视界存在下的热力学不依赖于半经典处理。强调了与视界热力学的关系以及视界面积作为熵的作用。
We compute the transition amplitudes between charged particles of mass $M$ and $m$ accelerated by a constant electric field and interacting by the exchange of quanta of a third field. We work in second quantization in order to take into account both recoil effects induced by transitions and the vacuum instability of the charged fields. In spite of both effects, when the exchanged particle is neutral, the equilibrium ratio of the populations is simply $\mathrm{exp}[\ensuremath{\pi}{(M}^{2}\ensuremath{-}{m}^{2})/eE].$ Thus, in the limit $(M\ensuremath{-}m)/\stackrel{\ensuremath{\rightarrow}}{M}0,$ one recovers Unruh's result characterized by the temperature $a/2\ensuremath{\pi}$ where $a$ is the acceleration. When the exchanged particle is charged, its vacuum instability prevents a simple description of the equilibrium state. However, in the limit wherein the charge of the exchanged particle tends to zero, the equilibrium distribution is once more Boltzmannian, but characterized not only by a temperature but also by the electric potential felt by the exchanged particle. This work therefore confirms that thermodynamics in the presence of horizons does not rely on a semiclassical treatment. The relationship with horizon thermodynamics and the role of the horizon area as an entropy are stressed.