Nonperturbative Ambiguities and the Reality of Resurgent Transseries
Nonperturbative Ambiguities and the Reality of Resurgent Transseries
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DOI：
10.1007/s00220-014-2165-z
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发表时间：
2015-04-01
影响因子：
2.4
通讯作者：
Schiappa, Ricardo
中科院分区：
文献类型：
--
作者：
Aniceto, Ines;Schiappa, Ricardo
从量子力学到量子场论，从规范理论到弦论，在广泛的量子理论背景下，复波莱尔平面上的奇点，通常与瞬子或重正子相关，使微扰理论定义不清，因为它们会引起非微扰的歧义。这些模糊性与扰动理论中的积分轮廓的选择有关，沿着复波莱尔平面中的（奇异）斯托克斯方向（使得扰动展开沿着任何斯托克斯线都是非波莱尔可和的）。最近，研究表明，解决这些问题的适当框架是复兴分析和跨系列框架。在这种情况下，取消所有的非微扰模糊性被证明是一个后果，选择transseries中位数remmation作为适当的家庭的明确的真实的解决方案沿着耦合常数真实的轴。虽然中值重算对于单参数transseries很容易实现，但是一旦考虑更一般的多参数transseries，该过程就变得高度依赖于正确理解复波莱尔平面中的斯托克斯跃迁。特别是，所有的斯托克斯系数现在必须是已知的，以便明确地实现多参数中值插值。在量子理论的物理观测量由复活函数和transseries描述的情况下，本文描述的方法显示了如何消除非微扰模糊性，并从微扰理论出发非微扰地定义这些观测量。沿着的方式，结构的结果有关复苏transseries也得到了。
In a wide range of quantum theoretical settings-from quantum mechanics to quantum field theory, from gauge theory to string theory-singularities in the complex Borel plane, usually associated to instantons or renormalons, render perturbation theory ill-defined as they give rise to nonperturbative ambiguities. These ambiguities are associated to choices of an integration contour in the resummation of perturbation theory, along (singular) Stokes directions in the complex Borel plane (rendering perturbative expansions non-Borel summable along any Stokes line). More recently, it has been shown that the proper framework to address these issues is that of resurgent analysis and transseries. In this context, the cancelation of all nonperturbative ambiguities is shown to be a consequence of choosing the transseries median resummation as the appropriate family of unambiguous real solutions along the coupling-constant real axis. While the median resummation is easily implemented for one-parameter transseries, once one considers more general multi-parameter transseries the procedure becomes highly dependent upon properly understanding Stokes transitions in the complex Borel plane. In particular, all Stokes coefficients must now be known in order to explicitly implement multi-parameter median resummations. In the cases where quantum-theoretical physical observables are described by resurgent functions and transseries, the methods described herein show how one may cancel nonperturbative ambiguities, and define these observables nonperturbatively starting out from perturbation theory. Along the way, structural results concerning resurgent transseries are also obtained.