We study a planar bubble wall that is traveling at an ultrarelativistic speed through a thermal plasma. This situation may arise during a first-order electroweak phase transition in the early universe. As particles cross the wall, it is assumed that their mass grows from ma to mb, and they are decelerated causing them to emit massless radiation (mc = 0). We are interested in the momentum transfer to the wall, the thermal pressure felt by the wall, and the resultant terminal velocity of the wall. We employ the semiclassical current radiation (SCR) formalism to perform these calculations. An incident-charged particle is treated as a point-like classical electromagnetic current, and the spectrum of quantum electromagnetic radiation (photons) is derived by calculating appropriate matrix elements. To understand how the spectrum depends on the thickness of the wall, we explore simplified models for the current corresponding to an abrupt and a gradual deceleration. For the model of abrupt deceleration, we find that the SCR formalism can reproduce the Ptherm ∝ γ0w scaling found in earlier work by assuming that the emission is soft, but if the emission is not soft the SCR formalism can be used to obtain Ptherm ∝ γ2w instead. For the model of gradual deceleration, we find that the wall thickness Lw enters to cutoff the otherwise log-flat radiation spectrum above a momentum of ∼ γ2w / Lw, and we discuss the connections with classical electromagnetic bremsstrahlung.

中文翻译：

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半经典形式对超相对论气泡的热压力


我们研究的是一个平面气泡壁，它以超相对论的速度穿过热等离子体。这种情况可能出现在早期宇宙的一阶电弱相变期间。当粒子穿过壁时，假设它们的质量从 马 增长到 mb，并且它们减速导致它们发出无质量辐射 （mc = 0）。我们对向壁的动量传递、壁感受到的热压以及由此产生的壁的终端速度感兴趣。我们采用半经典电流辐射 （SCR） 形式来执行这些计算。将带入射电荷的粒子视为点状经典电磁流，并通过计算适当的矩阵元素得出量子电磁辐射（光子）的频谱。为了了解频谱如何取决于壁的厚度，我们探索了对应于突然和逐渐减速的电流的简化模型。对于突然减速的模型，我们发现 SCR 形式可以通过假设发射是软的来再现早期工作中发现的 Ptherm ∝ γ0w 缩放，但如果发射不是软的，则可以使用 SCR 形式来获得 γ2w ∝ Ptherm。对于逐渐减速的模型，我们发现壁厚 Lw 进入以切断 ∼ γ2w / Lw 动量以上的对数平坦辐射光谱，我们讨论了与经典电磁轫致辐射的联系。