论文标题
同型代数的标量场理论的相关函数
Correlation functions of scalar field theories from homotopy algebras
论文作者
论文摘要
我们介绍了使用量子$ a_ \ infty $代数在扰动理论中标量场理论的相关函数的表达式。我们的表达方式是高度显式的，可用于欧几里得空间和包括量子力学的Minkowski空间中的理论。在给定的扰动理论顺序下的相关函数可以在不使用规范量化或路径积分的情况下通过代数计算，我们以$φ^3 $理论明确证明它。我们表明，基于量子$ a_ \ infty $代数的表达式形式的直接结果满足了schwinger-dyson方程。
We present expressions for correlation functions of scalar field theories in perturbation theory using quantum $A_\infty$ algebras. Our expressions are highly explicit and can be used for theories both in Euclidean space and in Minkowski space including quantum mechanics. Correlation functions at a given order of perturbation theory can be calculated algebraically without using canonical quantization or the path integral, and we demonstrate it explicitly for $φ^3$ theory. We show that the Schwinger-Dyson equations are satisfied as an immediate consequence of the form of the expressions based on quantum $A_\infty$ algebras.
