标题： 从同伦代数中得到的非微扰关联函数 显示英文标题

标题： Nonperturbative correlation functions from homotopy algebras

摘要： 基于arXiv:2203.05366、arXiv:2305.11634和arXiv:2305.13103中量子$A_\infty$代数的相关函数公式，要求我们将作用量分为自由部分和相互作用部分。我们提出了一种不涉及这种划分的新公式。新公式要求我们选择一个满足运动方程的解，该解不必是实数，我们认为该公式给出了在我们所选解相关的Lefschetz锥体上计算的相关函数。我们的公式在微扰理论中正确再现了相关函数，但它可以非微扰地有效，并且我们提供了零维标量场理论在欧几里得情况和洛伦兹情况下有限耦合常数相关函数的数值证据。当理论仅由一个Lefschetz锥体组成时，通过选择对应于该锥体的解，我们的公式可以给出理论的相关函数。当理论由多个Lefschetz锥体组成时，我们需要计算这些锥体的配分函数的比值，并且我们在即将发表的论文中描述了一种基于量子$A_\infty$代数的此类计算方法。 显示英文摘要

摘要： The formula for correlation functions based on quantum $A_\infty$ algebras in arXiv:2203.05366, arXiv:2305.11634, and arXiv:2305.13103 requires us to divide the action into the free part and the interaction part. We present a new form of the formula which does not involve such division. The new formula requires us to choose a solution to the equations of motion which does not have to be real, and we claim that the formula gives correlation functions evaluated on the Lefschetz thimble associated with the solution we chose. Our formula correctly reproduces correlation functions in perturbation theory, but it can be valid nonperturbatively, and we present numerical evidence for scalar field theories in zero dimensions both in the Euclidean case and the Lorentzian case that correlation functions for finite coupling constants can be reproduced. When the theory consists of a single Lefschetz thimble, our formula gives correlation functions of the theory by choosing the solution corresponding to the thimble. When the theory consists of multiple Lefschetz thimbles, we need to evaluate the ratios of the partition functions for those thimbles and we describe a method of such evaluations based on quantum $A_\infty$ algebras in a forthcoming paper.