发表机构
University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过Wilson线修饰的标量场算符，在标量QED中发展规范与洛伦兹不变的微扰方法，揭示带电态的超选择结构及红外粒子行为，并证明红外粒子标度律在宽时间窗口内稳健存在。
AI 中文摘要
我们发展了一种显式规范与洛伦兹不变的微扰计算方法，用以研究标量量子电动力学中由Wilson线修饰的标量场算符所产生的带电态在有限时间和距离上的演化。通过Osterwalder-Schrader反射和欧几里得粘合，两个修饰态的重叠被表示为修饰算符的欧几里得两点函数，随后在重整化微扰论中，以Stueckelberg光子质量作为规范、BRST和洛伦兹不变的红外截断对其进行计算。这使得带电扇区的若干结构特征得以显式且以闭式形式计算，而这些特征迄今主要通过非微扰或代数论证才能触及。我们发现，由非平行Wilson线修饰的态是“云正交”的。它们的重叠随红外调节器以幂律消失，其指数仅取决于两条修饰线之间的夹角，并且是尖点反常维度的红外类比，区别在于当带电物质具有质量间隙时该指数是单圈精确的。因此，带电态由其修饰的取向进行超选择。在超选择扇区内，两点函数是红外有限的，但展现出红外粒子。质壳极点被支割边缘所取代。结果，修饰电荷的渐近扩展是固有时上的幂律，其指数可单圈精确计算，取决于修饰和运动方向。我们表明，尽管云正交性和红外粒子各自对基本红外截断极其敏感，红外粒子的标度律在宽泛的固有时窗口内仍然持续存在。
英文摘要
We develop a manifestly gauge and Lorentz invariant perturbative calculus to study the finite time and distance evolution of the electrically charged states created by Wilson-line-dressed scalar field operators in scalar quantum electrodynamics. By an Osterwalder-Schrader reflection and Euclidean gluing, the overlap of two dressed states is expressed as a Euclidean 2 point function of dressed operators, which is then evaluated in renormalized perturbation theory with a Stueckelberg photon mass as a gauge, BRST and Lorentz invariant infrared cutoff. This renders explicit and computable in closed form several structural features of the charged sector that have so far been accessible mainly through non-perturbative or algebraic arguments. We find that states dressed by non-parallel Wilson lines are ``cloud orthogonal". Their overlap vanishes as a power of the infrared regulator, with an exponent that depends only on the angle between the two dressings and is an infrared analogue of the cusp anomalous dimension with the difference that it is one-loop exact whenever the charged matter is mass-gapped. Charged states are thereby superselected by the orientation of their dressing. Within a superselection sector the 2 point function is infrared finite but exhibits the infraparticle. The mass shell pole is replaced by the edge of a branch cut. As a result, the asymptotic spread of a dressed charge is a power law in proper time with a one-loop-exact computable exponent depending on the dressing and on the direction of motion. We show that although cloud orthogonality and the infraparticle are each extremely sensitive to fundamental infrared cutoffs, the infraparticle scaling law persists across a wide window of proper time.
Comments33 pages, 3 figures, some typos fixed and a few clarifying remarks added
