发表机构
Clausthal Technical University（Clausthal工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了因果谐振腔中模式量子的自引力，证明线性化量子引力的单圈积分有限，并由此从普朗克与红外尺度涌现出量级为H^2/G的真空能量密度，可解释暗能量效应。
AI 中文摘要
微扰量子引力存在紫外发散，并且如特胡夫特和韦尔特曼所示，它是不可重整化的。最近一种基于客体相对论且洛伦兹不变的内部电磁模式加权方法，使得量子电动力学的选定单圈贡献无需抵消项即可变为有限。在此，这种加权是被推导出来的而非被假设的：因果性定义了一个以哈勃半径为界并在每个惯性系中重新定义的模式谐振腔，而每个模式量子的自引力使其谱发生形变。应用于线性化引力时，引力子自耦合在普朗克波数处达到一阶量级，因此一个圈可用的模式内容在其之上被抑制。任何超过由费曼图确定的阈值的抑制都使得单圈积分有限；无需引入截断，也无需推导普朗克尺度以上的模式结构。对于纯引力，相同的幂次计数可推广到每一圈阶，并且对于任何具有多于一个顶点的拓扑，领先的抑制已经满足由此产生的条件；仅有一类单顶点插入被排除。在单圈阶，比安基恒等式扮演了沃德恒等式的角色，并且两个惯性系谐振腔之间的变换是幺正的。相同的有限模式内容仅从普朗克尺度和因果红外波数就产生量级为H^2/G的真空能量密度，其符号和大小与观测一致。一个追踪瞬时膨胀速率的贡献是引力常数的精确重标度，并被原初核合成所排除，因此模式基在任何惯性系中都必须被冻结；将其参照于稳态德西特视界可将剩余系数固定为几何值6/π，并使得引力真空涨落的能量密度值成为可能，该值可被解释为暗能量效应的起源。
英文摘要
Perturbative quantum gravity is ultraviolet divergent and, as shown by 't Hooft and Veltman, non-renormalizable. A recent object-relative, Lorentz-invariant weighting of internal electromagnetic modes renders selected one-loop contributions of quantum electrodynamics finite without counterterms. Here that weighting is derived rather than postulated: causality defines a mode resonator bounded by the Hubble radius and re-defined in every inertial frame, and the self-gravitation of each mode quantum deforms its spectrum. Applied to linearized gravity, the graviton self-coupling reaches order unity at the Planck wave number, so that the mode content available to a loop is suppressed beyond it. Any suppression exceeding a threshold fixed by the diagram renders the one-loop integrals finite; no cutoff is imposed and no mode structure above the Planck scale need be derived. For pure gravity the same power counting extends to every loop order, and the leading suppression already meets the resulting condition for every topology with more than one vertex; a single class of single-vertex insertions is excluded. The Bianchi identity takes the role of the Ward identity at one loop, and the transformation between the resonators of two inertial frames is unitary. The same finite mode content yields a vacuum energy density of order H^2/G, of the observed sign and magnitude, from the Planck and causal infrared wave numbers alone. A contribution tracking the instantaneous expansion rate is an exact rescaling of the gravitational constant and is excluded by primordial nucleosynthesis, so the mode basis must be frozen in any inertial system; referring it to the stationary de Sitter horizon fixes the remaining coefficient to the geometric value 6/pi and makes a value for the energy density of gravitational vacuum fluctuations possible which can be interpreted as origin of the dark-energy effect.
Comments23 pages
