We propose a new formula for the star product in deformation quantization of Poisson structures related in a specific way to a variational problem for a function S , interpreted as the action functional. Our approach is motivated by perturbative algebraic quantum field theory (pAQFT). We provide a direct combinatorial formula for the star product, and we show that it can be applied to a certain class of infinite-dimensional manifolds (e.g. regular observables in pAQFT). This is the first step towards understanding how pAQFT can be formulated such that the only formal parameter is $$\hbar $$ ħ , while the coupling constant can be treated as a number. In the introductory part of the paper, apart from reviewing the framework, we make precise several statements present in the pAQFT literature and recast these in the language of (formal) deformation quantization. Finally, we use our formalism to streamline the proof of perturbative agreement provided by Drago, Hack, and Pinamonti and to generalize some of the results obtained in that work to the case of a nonlinear interaction.

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相互作用量子场论中的明星产品

我们为泊松结构变形量化中的星积提出了一个新公式，该公式以特定方式与函数 S 的变分问题相关，解释为动作泛函。我们的方法受到微扰代数量子场论 (pAQFT) 的启发。我们为星积提供了一个直接的组合公式，并表明它可以应用于某一类无限维流形（例如 pAQFT 中的常规可观察量）。这是理解 pAQFT 如何公式化的第一步，使得唯一的形式参数是 $$\hbar $$ ħ ，而耦合常数可以被视为一个数字。在论文的介绍部分，除了回顾框架之外，我们在 pAQFT 文献中做出了精确的几个陈述，并用（正式）变形量化的语言重新定义了这些陈述。最后，我们使用我们的形式来简化 Drago、Hack 和 Pinamonti 提供的微扰一致性证明，并将该工作中获得的一些结果推广到非线性交互的情况。