We study the effects of Goldstone modes on the stability of the vacuum in a $U(1)$ theory for a complex scalar field. The dynamics of the field resemble those of Keplerian motion in the presence of time-dependent friction, whose equations of motion imply a conserved quantity, L, reminiscent of conserved angular momentum. They also imply a persistent infinite barrier at $\rho =0$ and a divergent field value at the origin of coordinates in flat spacetime, rendering any solution physically unattainable. However, in a spacetime punctured at the origin of coordinates, we find finite-action solutions to the equations of motion, which correspond to the size of the hole $a_0$, which in turn determines the tunnelling point ${\rho }_0$ and L. We find that the rates of vacuum decay get drastically enhanced by many orders of magnitude for all possible orderings in which the false and true vacua are placed in the potential. Finally, we show how Goldstone modes provide the necessary energy to overcome drag forces yielding finite-action solutions for any potential, including those that no such solutions exist for real scalar fields.

我们研究了Goldstone模式对真空中真空稳定性的影响 $ü（\mathrm{1个}）$复杂标量场的理论。在存在时变摩擦的情况下，该场的动力学类似于开普勒运动，其运动方程式表示一个守恒量L，使人想起了守恒角动量。它们还暗示着在$\rho =0$以及在平面时空中坐标原点处的发散字段值，使任何解决方案在物理上都无法实现。但是，在以坐标原点为起点的时空中，我们发现了运动方程的有限作用解，该解对应于孔的大小${\mathrm{一种}}_0$，这反过来又确定了隧道点 ${\rho }_0$和大号。我们发现，对于所有将假真空和真真空置于潜在位置的可能排序，真空衰减速率都大大提高了多个数量级。最后，我们展示了戈德斯通模式如何提供必要的能量来克服阻力，从而为任何势能产生有限作用的解决方案，包括那些对于实际标量场不存在此类解决方案的解决方案。