荷兰乌得勒支大学Mick van Vliet团队近日研究了论量子场论的复杂性。2025年6月24日出版的《高能物理杂志》发表了这项成果。

研究组通过提出量子场论中包含的信息及其可观测值的度量，启动了对量子场论复杂性的研究。他们证明，从最小断言开始，人们自然会通过两个整数来衡量复杂性，称为格式和度，这两个整数表征了指定理论或可观测值所需的函数和域的信息内容。该提案的优点是它适用于任何物理量，因此可用于分析单个QFT内的复杂性，以及研究QFT的整个空间。 

研究组在微扰理论、对称性和重整化群的背景下讨论了该方法的物理解释。关键应用包括检测可观察性的复杂性降低，例如由于代数关系，以及在考虑极限时理解简单性的出现。研究组构造的数学基础在于尖锐的o-minimaly框架，这确保了所提出的复杂性度量具有从一致性和普适性推断出的一般性质。

附：英文原文

Title: On the complexity of quantum field theory

Author: Grimm, Thomas W., van Vliet, Mick

Issue&Volume: 2025-06-24

Abstract: We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two integers, called format and degree, which characterize the information content of the functions and domains required to specify a theory or an observable. The strength of this proposal is that it applies to any physical quantity, and can therefore be used for analyzing complexities within an individual QFT, as well as studying the entire space of QFTs. We discuss the physical interpretation of our approach in the context of perturbation theory, symmetries, and the renormalization group. Key applications include the detection of complexity reductions in observables, for example due to algebraic relations, and understanding the emergence of simplicity when considering limits. The mathematical foundations of our constructions lie in the framework of sharp o-minimality, which ensures that the proposed complexity measure exhibits general properties inferred from consistency and universality.

DOI: 10.1007/JHEP06(2025)215

Source: https://link.springer.com/article/10.1007/JHEP06(2025)215