Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a finite-element formulation. This approach is far more robust, versatile, and powerful than existing methods, thus allowing for more sophisticated computations and the study of problems that could not previously be tackled. Importantly, existing procedures, element libraries and shape functions, which have been developed throughout the years in the context of engineering analysis and partial differential equations, may be directly employed for this purpose.

翻译：泛函积分是现代理论的核心工具，其应用范围从量子力学、统计热力学延伸至生物学、化学和金融领域。本文提出了一种基于有限元形式的泛函积分新计算方法。该方法相比现有方法具有更强的鲁棒性、通用性和计算能力，从而支持更复杂的计算任务，并可研究此前无法解决的问题。值得关注的是，多年来在工程分析和偏微分方程领域发展出的现有程序、单元库和形函数均可直接用于此目的。