发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将广义迹动力学发展为量子、时空与引力临界涌现的可计算框架，通过多通道复合场论和代理系综验证关键诊断量，提出定量可证伪的有效理论。
AI 中文摘要
广义迹动力学（GTD）是一种关于aikyons（时空-物质原子）的确定性动力学，其近平衡统计力学产生量子动力学，而大的反自伴涨落驱动自发定域化和涌现的经典时空。我们分离两个独立的大极限：有限系统的长Connes时间粗粒化，条件性地产生量子Ward恒等式；以及集体奇异性所需的广泛多aikyon/大矩阵极限。我们将E8 x omega E8纲领的凝聚态类比转化为一个定量的、可证伪的有效框架。四个耦合的复合通道（双费米子定域化、几何焊接/洛伦兹-希格斯、规范不变的弱电、以及矩阵值味）定义了一个精确的磁化率矩阵和Legendre有效作用量，给出共同连续或一级相变的零模和自由能判据。我们以Schwinger-Keldysh形式提出非平衡问题，定义投影的涨落-耗散缺陷和Born概率的鞅条件，将牛顿常数识别为有序几何相的刚度，并给出Sakharov、约束BF、Jacobson、Padmanabhan和Verlinde引力描述成为同一基底极限的条件。一个受调控的双扇区代理系综（一个Myers变形的几何三重态耦合到一个物质矩阵，带有Grassmann调控的费米子扩展）表明选定的诊断量是可计算的：精确的Adler-Millard电荷守恒、多通道一级跳变、验证的涨落-耗散关系及其淬火缺陷，以及在涌现的二球面上的费米子谱维数d_s = 1.96。结果是一个计算纲领，而非完成的推导；下一步是GTD本身的多aikyon复合两点矩阵。
英文摘要
Generalized trace dynamics (GTD) is a deterministic dynamics of aikyons (atoms of space-time-matter) whose near-equilibrium statistical mechanics yields quantum dynamics, while large anti-self-adjoint fluctuations drive spontaneous localisation and emergent classical spacetime. We separate two independent large limits: long-Connes-time coarse-graining of a finite system, which conditionally yields the quantum Ward identities, and the extensive many-aikyon/large-matrix limit required for a collective singularity. We turn the condensed-matter analogy of the E8 x omega E8 programme into a quantitative, falsifiable effective framework. Four coupled composite channels (bifermionic localisation, geometric soldering/Lorentz-Higgs, gauge-invariant electroweak, and matrix-valued flavour) define an exact susceptibility matrix and Legendre effective action, giving zero-mode and free-energy criteria for a common continuous or first-order transition. We pose the nonequilibrium problem in Schwinger-Keldysh form, define a projected fluctuation-dissipation defect and the martingale condition for Born probabilities, identify Newton's constant with the stiffness of the ordered geometric phase, and give conditions under which the Sakharov, constrained-BF, Jacobson, Padmanabhan and Verlinde descriptions of gravity are limits of one substrate. A regulated two-sector surrogate ensemble (a Myers-deformed geometric triple coupled to a matter matrix, with a Grassmann-regulated fermionic extension) shows that selected diagnostics are calculable: exact Adler-Millard charge conservation, a multi-channel first-order jump, a verified fluctuation-dissipation relation and its quench defect, and a fermionic spectral dimension d_s = 1.96 on the emergent two-sphere. The result is a calculational programme, not a completed derivation; the next step is the many-aikyon composite two-point matrix for GTD itself.
Comments40 pages
