We study the fate of a false vacuum in the case of a potential that contains a portion which is quartic and unbounded. We first prove that an O(4) invariant instanton with the Coleman boundary conditions does not exist in this case. This, however, does not imply that the false vacuum does not decay. We show how the quantum fluctuations may regularize the singular classical solutions. This gives rise to a new class of O(4) invariant regularized instantons which describe the vacuum instability in the absence of the Coleman instanton. We derive the corresponding solutions and calculate the decay rate they induce.

中文翻译：

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量子涨落和新瞬子II：四次无限界

我们研究虚假真空的命运，该虚假真空的可能性包含四次且无界的部分。我们首先证明在这种情况下不存在具有Coleman边界条件的O（4）不变实例。但是，这并不意味着假真空不会衰减。我们展示了量子涨落如何使正则经典解正规化。这就产生了新的O（4）不变正则化瞬时类，它描述了在没有Coleman瞬时子的情况下的真空不稳定性。我们得出相应的解并计算它们引起的衰减率。