非相对论共形场论中的探测器
Detectors in Nonrelativistic Conformal Field Theories
- University of Chicago（芝加哥大学）
- The Abdus Salam ICTP（阿卜杜斯·萨拉姆理论物理中心）
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在非相对论共形场论中引入探测器算符，定义能量通量对速度的微分，研究其对称性并计算多点函数，推导非相对论Hofman-Maldacena界限，揭示Efimov三体态中的喷注结构。
AI中文摘要：
渐近通量中的关联是研究物理系统的主要实验手段之一。在相对论量子场论的背景下，用探测器算符形式化此类实验已取得显著进展。受这些成功的启发，本文开创了对非相对论共形场论（NRCFTs）中探测器算符的研究。在NRCFTs中，通量在角度和速度上均有分布，使得自然的探测器算符为能量通量对速度的微分，即$\mathcal{E}_v(\hat{n})$。我们提供了这些算符在NRCFTs中的非微扰定义，并研究了它们的对称性和代数。我们在代表性NRCFTs的多种少体和多体态中计算了这些探测器可观测量的一点函数，包括自由费米子以及幺正极限下的费米子。在相互作用的三体态中，它们展现出极其丰富的行为，反映了Efimov三体波函数，包括由于共振相互作用而形成的增强“喷注”结构。我们利用这些探测器，通过论证$\mathcal{E}_v(\hat{n})$的正性并将其应用于自旋1态，推导出Hofman-Maldacena共形对撞机界限的非相对论推广。我们概述了NRCFTs中探测器研究的若干未来方向，并讨论了如何在从冷原子到低能中子实验等多种实验平台上测量它们。
英文摘要：
Correlations in asymptotic fluxes provide one of the primary experimental means of studying physical systems. In the context of relativistic QFT, the formalization of such experiments in terms of detector operators has led to significant progress. Motivated by these successes, in this paper we initiate a study of detector operators in nonrelativistic conformal field theories (NRCFTs). In NRCFTs, fluxes are distributed in both angle and velocity, making the natural detector operator the energy flux differential in velocity, $\mathcal{E}_v(\hat{n})$. We provide non-perturbative definitions of these operators in NRCFTs, and study their symmetries and algebra. We calculate one-point functions of these detector observables in a variety of few and many body states of representative NRCFTs, including free fermions, as well as fermions at unitarity. In interacting three-body states, they exhibit a remarkably rich behavior reflective of the Efimov three-body wave-function, including the formation of an enhanced "jet" structure due to the presence of resonant interactions. We use these detectors to derive a nonrelativistic generalization of the Hofman-Maldacena conformal collider bounds by arguing for positivity of $\mathcal{E}_v(\hat{n})$, and imposing this in spin 1 states. We outline a number of future directions for the study of detectors in NRCFTs, and discuss how they can be measured in a variety of experimental platforms from cold atoms to low energy neutron experiments.
