发表机构
Department of Physics, Kyushu University; Quantum and Spacetime Research Institute (QuaSR), Kyushu University（九州大学物理系; 九州大学量子与时空研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用高阶微扰系数重新检验Suzuki-Yasuta公式，发现其在二维O(N)理论中随阶数收敛，并接近半经典近似结果。
AI 中文摘要
在20世纪90年代末，Suzuki和Yasuta提出了一个紧凑公式，该公式从真空能量密度的常规微扰系数（即真空气泡图）中提取$D$维$O(N)$ $\lambda(\phi^2)^2$理论（具有无界势）中假真空的每单位体积衰变率。其思想是将沿Borel变换不连续性的Borel积分所产生的虚部与真空能量密度的虚部等同起来。虽然该公式在$D=1$（即量子力学）时效果很好，但其在$D\geq2$时的有效性仍不清楚，因为当时只有$D=2$的前三个微扰系数可用，且结果未显示收敛迹象。在本文中，我们利用Serone、Spada和Villadoro获得的$D=2$、$N=1$的前七个非平凡微扰系数（直至九圈）重新审视了这一方法。按照这些作者的做法，我们在有限阶截断的Borel变换中引入两个可调参数，发现随着微扰阶数的增加，虚部趋于收敛，最后几阶的结果在百分之几的范围内一致。在耦合常数的中间范围，$3\lesssim\widetilde{g}\lesssim8$，该方法得到的虚部非常接近包含单圈行列式的领头阶半经典近似；它比Malatesta、Parisi和Rizzo计算的包含两圈修正的半经典结果大$10$--$20\\%$。
英文摘要
In the late 1990s, Suzuki and Yasuta proposed a compact formula that extracts the decay rate per unit volume of a false vacuum in the $D$-dimensional $O(N)$ $λ(ϕ^2)^2$ theory with an unbounded potential from conventional perturbative coefficients of the vacuum energy density, i.e., vacuum bubble diagrams. The idea was to identify the imaginary part arising from the Borel integral along the discontinuity of the Borel transform with that of the vacuum energy density. While the formula works quite well for~$D=1$, i.e., quantum mechanics, its validity remained unclear for~$D\geq2$ because only the first three perturbative coefficients for~$D=2$ were available and the result showed no sign of convergence. In the present paper, we reexamine this approach using the first seven nontrivial perturbative coefficients (up to nine loops) for~$D=2$ and~$N=1$ obtained by Serone, Spada, and~Villadoro. Introducing two tunable parameters in the finite-order truncated Borel transform following these authors, we find that the imaginary part converges as the perturbative order increases, with the last few orders agreeing to within a few percent. In the intermediate range of the coupling constant, $3\lesssim\widetilde{g}\lesssim8$, this approach yields an imaginary part rather close to the leading-order semi-classical approximation with the one-loop determinant; it is $10$--$20\%$ larger than the semi-classical result with the two-loop correction computed by Malatesta, Parisi, and~Rizzo.
Comments20 pages, 8 figures
