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arXiv 1504.04334hep-thgr-qc
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引力作用下量子隧穿中负模问题的解

Towards a Solution of the Negative Mode Problem in Quantum Tunnelling with Gravity

Michael Koehn, George Lavrelashvili, Jean-Luc Lehners

摘要:

在没有引力的情况下,我们可以证明隧穿瞬子在它们的涨落谱中只表现出一个负模。正是这种隧道负模式的存在,才保证了将这些解解释为介导亚稳态真空的衰变。在引力存在的情况下,情况要微妙得多,尤其是因为复同态不变性。这里出现了新的复杂情况:特别是,涨落的动力学项可以在瞬子的某处改变符号。我们表明,在这种情况下,模式功能保持非奇异的,隧道负模式继续存在。此外,当电势变化时,特征值连续变化,使得波动的动力学项切换符号。然而,负动力学项意味着额外存在一个无限的负模式塔,其意义和解释仍然难以捉摸。

英文摘要:

In the absence of gravity, one can prove that tunnelling instantons exhibit exactly one negative mode in their spectrum of fluctuations. It is precisely the existence of this tunnelling negative mode that warrants an interpretation of these solutions as mediating the decay of a metastable vacuum. In the presence of gravity the situation is much more subtle, not least because of diffeomorphism invariance. New complications arise here: in particular, the kinetic term of the fluctuations can change sign somewhere along the instanton. We show that in this case the mode functions remain non-singular, and the tunnelling negative mode continues to exist. Moreover, the eigenvalues vary continuously when the potential is varied such that the kinetic term of the fluctuations switches sign. However, the negative kinetic term implies the additional existence of an infinite tower of negative modes, whose significance and interpretation remain elusive.

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