引力作用下量子隧穿中的负模问题
Aspects of the negative mode problem in quantum tunneling with gravity
摘要：
一些描述真空衰变的解表现出灾难性的不稳定性。这个所谓的负模式问题在引力作用下的量子隧穿中被发现于34年前，尽管这些年来许多不同的小组都在研究这个问题，但它仍然没有得到解决。在这里，我们简要地总结了目前的状况的问题，并调查反弹的性质，数值和分析物理上有趣的潜力。在框架内的哈密顿方法，我们表明，一般多项式的潜力的负模式问题可能会出现在能量远低于普朗克质量，这表明负模式问题是不相关的物理在普朗克尺度。同时，我们发现，对于一个希格斯像潜在的，因为它出现在标准模型，问题并没有出现在现实值的潜力的参数，但只有在普朗克尺度。
英文摘要：
Some solutions describing vacuum decay exhibit a catastrophic instability. This, so-called negative mode problem in quantum tunneling with gravity, was discovered 34 years ago and in spite of the fact that in these years many different groups worked on this topic, it has still not been resolved. Here, we briefly summarize the current status of the problem and investigate properties of the bounces, numerically and analytically for physically interesting potentials. In the framework of the Hamiltonian approach we show that for generic polynomial potentials the negative mode problem could arise at energies much lower than the Planck mass, indicating that the negative mode problem is not related to physics at the Planck scale. At the same time we find that for a Higgs like potential, as it appears in the standard model, the problem does not appear at realistic values of the potential's parameters but only at the Planck scale.
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