We consider the decay of a false vacuum in circumstances where the methods suggested by Coleman run into difficulties. We find that in these cases quantum fluctuations play a crucial role. Namely, they naturally induce both ultraviolet and infrared cutoff scales, determined by the parameters of the classical solution, beyond which this solution cannot be trusted anymore. This leads to the appearance of a broad class of new O(4) invariant instantons, which would have been singular in the absence of an ultraviolet cutoff. We apply our results to a case where the potential is unbounded from below in a linear way and in particular show how the problem of small instantons is resolved by taking into account the inevitable quantum fluctuations.

中文翻译：

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量子涨落和新瞬时子I：线性无穷大势能

在科尔曼建议的方法遇到困难的情况下，我们考虑了虚假真空的衰减。我们发现，在这些情况下，量子涨落起着至关重要的作用。即，它们自然地诱发由经典解决方案的参数确定的紫外和红外截止尺度，超出此范围，该解决方案将不再值得信赖。这导致出现一类新的O（4）不变瞬时子，在没有紫外线截止的情况下它们将是单一的。我们将结果应用到电势从下方以线性方式不受限制的情况，并特别说明了如何通过考虑不可避免的量子涨落来解决小瞬间问题。