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Mukhanov, V. F.; Rabinovici, E.; Sorin, A. S.
Fortschritte der Physik, February 2021, 2021-02-00, 20210201, Volume: 69, Issue: 2Journal Article
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. The decay of a false vacuum is considered in circumstances where the methods suggested by Coleman run into difficulties. It is found 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. The results will be applied to a case where the potential is unbounded from below in a linear way. In particular it will be shown how the problem of small instantons is resolved by taking into account the inevitable quantum fluctuations.
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