发表机构
Universidad de Cantabria (UC)（坎塔布里亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究空间截断 $\phi^4_2$ 的构造性积分，用指数-动机周期序列表示，分析伽罗瓦变换对配分周期发散和固定可观测量极限的影响，并给出无有界实现时极限不成比例的反例。
AI 中文摘要
我们用指数-动机周期的序列来表示空间截断 $\phi^4_2$ 中的构造性积分。对于非零空间截断，单个伽罗瓦变换会使得配分周期在满足构造性估计的每一序列逼近中模发散。对于固定的截断表示，我们刻画了在自由场的 $L^1$ 空间上允许有界实现的变换子群，并证明在该子群上所有固定可观测量的极限都是其物理值的公共标量倍数。一个单变量四次例子表明，所有变换后的固定可观测量序列可以在没有这种有界实现的情况下收敛，且其极限与物理值不成比例。
英文摘要
We represent constructive integrals in spatially cut-off $ϕ^4_2$ by sequences of exponential-motivic periods. For a nonzero spatial cutoff, a single Galois transformation makes the partition periods diverge in modulus along every sequence of approximations satisfying the constructive estimates. For a fixed cutoff presentation, we characterize the subgroup of transformations admitting a bounded realization on the free field's $L^1$ space and prove that all fixed-observable limits on this subgroup are a common scalar multiple of their physical values. A one-variable quartic example shows that all transformed fixed-observable sequences can converge without such a bounded realization, with limits that are not proportional to the physical values.
