AI 中文总结
研究在有限体积下构建正弦 - 戈登测度及其重整化有效势直至第七阈值的问题，核心方法是借助弱随机控制问题、弱FBSDE及多极梅耶展开对重整化流方程分析，在次临界区域有完整逐阶分析贡献。
AI 中文摘要
我们在有限体积下构建了正弦 - 戈登测度及其重整化有效势直至第七阈值。该构造依赖于一个弱随机控制问题、其相关的弱FBSDE以及使用多极梅耶展开对重整化流方程的分析。分析是完全归纳的，且在次临界区域\(\beta^{2}<8\pi\)中进行了完整的逐阶分析。
英文摘要
We construct the sine-Gordon measure and its renormalized effective potential in finite volume up to the seventh threshold. The construction relies on a weak stochastic control problem, its associated weak FBSDE, and an analysis of the renormalization flow equation using a multipole Mayer expansion. The analysis is fully inductive, and we include a complete order-by-order analysis in the subcritical regime $β^{2}<8π$.
Comments82 pages
