（反）德西特空间中的复世界线瞬子
Complex Worldline Instantons in (Anti-)de Sitter Space
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中文总结 AI 辅助
本文研究二维带电粒子世界线路径积分的复鞍点，揭示瞬子作用仅由拓扑数据决定，并在反德西特空间中受无量纲比值控制，为瞬子分类提供新规则。
中文摘要 AI 辅助
我们研究了在二维极大对称背景中，由均匀电场贯穿的带质量带电粒子的世界线路径积分的复鞍点。在世界线形式中，我们表明半经典鞍点通常需要对目标时空和固有时参数两者都进行复化。由此得到的解包含一个单一复族的两片，由固有时演化的方向区分。沿虚固有时演化的一片所携带的作用通常控制非微扰效应的指数抑制，而沿实固有时演化的一片可能编码额外的复相位，这些相位负责鞍点之间的量子干涉。将该族视为一个整体，我们给出了一种构造和分类所有拓扑不等价瞬子扇区的规则，并发现世界线作用仅依赖于它们的拓扑数据，即围绕紧致方向和某些孤立奇点的绕数。此外，在反德西特时空中，解的定性结构由无量纲比值 $R |eE|/m$（$R$ 为曲率半径）决定，该比值区分了亚极值、极值和超极值区域。相比之下，在德西特时空中没有类似的区分——瞬子对该比值不敏感——在明可夫斯基时空中也没有，后者完全没有曲率尺度。我们还将作用重新表述为相关（非守恒）共轭动量的留数之和，使得哪些解析数据控制每个贡献变得清晰。最后，我们讨论了在各种局部补丁中构建的解提升到全局（反）德西特空间时出现的微妙之处。这些对哪些鞍点原则上可以贡献于单圈路径积分施加了进一步的必要条件。
英文摘要
We study complex saddle points of the worldline path integral for massive charged particles in two-dimensional maximally symmetric backgrounds threaded by homogeneous electric fields. Within the worldline formalism, we show that the semiclassical saddles generically require complexifying both the target spacetime and the proper-time parameter. The resulting solutions comprise two slices of a single complex family, distinguished by the direction of proper-time evolution. The one evolving in imaginary proper time carries an action that typically controls the exponential suppression of non-perturbative effects, while that evolving in real proper time may encode additional complex phases responsible for quantum interference between saddles. Treating this family as a whole, we give a prescription for constructing and classifying all topologically inequivalent instanton sectors, and we find that the worldline action depends only on their topological data, namely winding numbers around the compact directions and certain isolated punctures. Moreover, in Anti-de Sitter spacetime, the qualitative structure of the solutions is governed by the dimensionless ratio $R |eE|/m$ ($R$ being the curvature radius), which distinguishes sub-extremal, extremal, and super-extremal regimes. By contrast, no analogous distinction occurs in de Sitter---where the instantons are insensitive to this ratio---or in Minkowski spacetime, which lacks a curvature scale altogether. We also recast the action as a sum over residues of the relevant (non-conserved) conjugate momentum, making transparent which analytic data control each contribution. Finally, we discuss the subtleties that arise when solutions built in various local patches are lifted to global (Anti-)de Sitter space. These impose further necessary conditions on which saddles can in principle contribute to the one-loop path integral.
发表机构
- University of Chicago（芝加哥大学）
- Leinweber Institute for Theoretical Physics, University of Chicago（芝加哥大学莱因韦伯理论物理研究所）
- Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）
- Jefferson Physical Laboratory, Harvard University（哈佛大学杰斐逊物理实验室）
- Department of Astronomy & Astrophysics, University of Chicago（芝加哥大学天文学与天体物理学系）
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