Resurgence theory, ghost-instantons, and analytic continuation of path integrals
Resurgence theory, ghost-instantons, and analytic continuation of path integrals
复制标题
复兴理论、鬼瞬间和路径积分的解析延拓
DOI：
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发表时间：
2013
影响因子：
5.4
通讯作者：
M. Ünsal
中科院分区：
文献类型：
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作者：
G. Basar;G. Dunne;M. Ünsal
一般的量子力学或量子场论系统在路径积分公式中都有真实的和复鞍（瞬子和虚瞬子）。复苏渐近分析意味着这两种类型的鞍有助于物理观测，即使复杂的鞍不在积分路径上，即，相关的斯托克斯乘数为零。我们明确地表明，瞬子反瞬子和鬼反鬼鞍都影响周围的微扰真空膨胀。我们研究了一个自对偶模型，其中的解析延续的配分函数的负值的耦合常数给出了一个病态的指数增长，但同伦独立的组合的集成周期（Lefschetz顶针）的结果在一个明智的理论。积分周期的这两种选择与量子相变有关。在我们的建设中的一般想法可能会提供新的见解非微扰QFT，弦理论，量子引力和量子相变理论。
A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost-anti-ghost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.