We compute the vacuum polarization energy of kink solitons in the $\phi^{8}$ model in one space and one time dimensions. There are three possible field potentials that have eight powers of $\phi$ and that possess kink solitons. For these different field potentials we investigate whether the vacuum polarization destabilizes thesolitons. This may particularly be the case for those potentials that have degenerate ground states with different curvatures in field space yielding different thresholds for the quantum fluctuations about the solitons at negative and positive spatial infinity. We find that destabilization occurs in some cases, but this is not purely a matter of the field potential but also depends on the realized soliton solution for that potential. One of the possible field potentials has solitons with different topological charges. In that case the classical mass approximately scales like the topological charge. Even though destabilization precludes robust statements, there are indications that the vacuum polarization energy does not scale as the topological charge.

中文翻译：

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φ8 模型中孤子的量子校正

我们在 $\phi^{8}$ 模型中在一个空间和一个时间维度中计算扭结孤子的真空极化能量。存在三种可能的场势，它们具有 $\phi$ 的 8 次幂并且具有扭结孤子。对于这些不同的场势，我们研究真空极化是否会使孤子不稳定。对于那些具有在场空间中具有不同曲率的简并基态的势，这可能特别是这种情况，这些势在负空间和正空间无穷远处产生关于孤子的量子涨落的不同阈值。我们发现在某些情况下会发生不稳定，但这不仅仅是场势的问题，还取决于该势的已实现孤子解。一种可能的场势具有具有不同拓扑电荷的孤子。在那种情况下，经典质量近似地像拓扑电荷一样缩放。尽管不稳定排除了可靠的陈述，但有迹象表明真空极化能量不会随着拓扑电荷而缩放。