High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings, motivated by models in lattice gauge theory from quantum field theory. A novel element of this work is the potential benefit in using lattice cubature rules. The group structure within lattice rules combined with the special structure in the physics integrands may allow efficient computations based on Fast Fourier Transforms. Applications to the quantum mechanical rotor and compact $U(1)$ lattice gauge theory in two and three dimensions are considered.

中文翻译：

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格子遇到格子：格子体积在格子规范理论模型中的应用

高维积分在包括量子物理学在内的许多研究领域中都很丰富。本文的目的是开发有效的递归策略来解决一类具有特殊乘积结构和低阶耦合的高维积分，其动机是由量子场论中的晶格规范理论模型驱动的。这项工作的一个新元素是使用晶格体积规则的潜在好处。晶格规则内的群结构与物理被积函数中的特殊结构相结合，可以允许基于快速傅立叶变换的高效计算。考虑了在二维和三维空间中量子机械转子和紧凑的 $U(1)$ 格子规范理论的应用。