面向受控爱因斯坦响应的量子引力关系量子因果过程
Relational Quantum Causal Processes toward Quantum Gravity with Controlled Einstein Response
AI总结：
该研究在固定物理傅里叶带上构建受控基准，推导量子引力相关可观测量，得到固定带闭合定理，为非微扰闭合提供可复现基准。
AI中文摘要：
微观量子引力模型的核心挑战在于，从一个细化的量子族中推导几何与引力可观测量，且无需在每个界面改变动力学或拟合新系数。我们在声明的固定物理傅里叶带上构建了一个受控基准。对于每个空间调节器，一个有限希尔伯特空间相互作用哈密顿量定义了幺正完全正过程与欧几里得施温格泛函。其谱和源导数决定了洛伦兹间隙、连通四阶响应、混合物质-几何响应、动态几何核、诱导牛顿系数，以及进入半经典FLRW演化的量子物质应力。两个不等价的空间符号满足解析二阶和四阶界，并收敛到同一个极限哈密顿量。杜哈梅尔（Duhamel）与魏尔（Weyl）不等式、均匀间隙、解析微扰理论以及核余项估计给出了共同的固定带调节器极限。在声明的局域协变FLRW二阶导数扇区内，度规源唯一确定了正的诱导牛顿系数，而非将其作为界面拟合项。直接对角化独立得到非零的连通四阶响应与非拟合的无量纲谱组合。激发间隙为半经典弗里德曼轨迹提供了守恒应力张量。这是一个同家族固定带闭合定理，而非全带QFT或完整量子引力。两模态带、有限振子截断、协变二阶导数扇区以及半经典爱因斯坦方程为输入，该工作未构建量子度规希尔伯特空间、量子BV测度、拓扑变化控制或自主扇区选择。结果提供了可复现的基准，并分离出非微扰闭合所需的进一步定理。
英文摘要：
We construct a finite-Hilbert interacting quantum model in which matter and geometric response are generated by a single Schwinger functional along one spatial refinement. Two inequivalent discretizations converge analytically to the same Hamiltonian on a fixed physical Fourier band, with second- and fourth-order regulator bounds. The common limit determines the excitation gap, connected nonlinear matter response, mixed matter-geometry susceptibility, and low-frequency geometric kernel. Within a prescribed covariant two-derivative FLRW sector, the latter fixes a positive induced Newton coefficient without an additional normalization parameter. The same spectral data define a conserved excitation stress and a regulator-stable semiclassical Friedmann trajectory. These results establish a common regulator limit for interaction, response, and backreaction within one microscopic family. The construction is restricted to a two-mode Fourier band, a finite oscillator cutoff, and a prescribed semiclassical gravitational sector; an interacting all-band quantum field theory with dynamical geometry is not constructed here.
