发表机构
Northwestern Polytechnical University（西北工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种守恒律引导的量子场论粗粒化分类框架，明确算符分类判据，建立局域算符一般分类并经多系统验证，其逻辑结构与经典统计物理中推导流体方程的策略平行。
AI 中文摘要
本文提出一种守恒律引导的量子场论粗粒化操作分类框架。粗粒化在费曼图层面产生选择作用：具有非零动量转移的图被振荡因子压制，零动量转移的梯子图可通过几何级数重求和累积，从而产生谱极点，而单泡拓扑仅对连续谱有贡献。守恒律主导该分类：对于受Ward恒等式保护的算符，其零动量处的矩阵元必然非零；对于受BRST对称性保护的算符，Slavnov-Taylor恒等式不提供强制压制，这两种情况的代数保证强度存在差异；对于未受保护的算符，注入项消失，谱函数保持连续，且单泡贡献的符号由自旋统计决定，正号会导致梯子重求和中的放大反馈，负号则导致压制反馈。注入项的非零性与单泡贡献的符号这两个属性构成了该分类的定义判据。作为直接应用，本文在涌现框架内建立了局域算符的一般分类，并在八个物理道和三个已知可解系统上进行了验证。该框架指明每个算符可能的涌现路径，而临界条件是否达到则留待独立的非微扰计算确定。该分类的逻辑结构与经典统计物理中从分子动理论推导流体方程的策略平行。
英文摘要
Coarse-graining should retain the response to the perturbations and observations of interest. We study this requirement for systems defined by generating operations and observation maps. Equality of all allowed future outputs defines an observation-sufficient quotient; fibre consistency gives differentiable descent for bounded surjective linear maps between Banach spaces. Linearising the state equation and the observation together produces a response whose kernel, source, readout and direct term transform consistently under coarse-graining. We derive an exact comparison identity valid also for noninvertible coarse maps. Eliminating residual states yields a memory representation and, under decay bounds, controlled finite-memory approximations. For isolated critical modes, analytic Fredholm theory gives the pole and visibility conditions; reciprocal realisations with a positive crossing matrix have positive finite-rank residues. An arithmetic merge and a reflecting heat protocol illustrate these results by explicit calculations. Gaussian averaging and quantum-field-theory channels provide further realisations, including the identification of response poles with vacuum spectral atoms under matched spectral hypotheses.
Comments67 pages, no figures. The CGC source code is included as ancillary files and is also available at https://github.com/bookwormseagull1980/Conservation-Guided-assification
