Abstract
We present expressions for correlation functions of scalar field theories in perturbation theory using quantum A∞ 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 φ3 theory. We show that the Schwinger-Dyson equations are satisfied as an immediate consequence of the form of the expressions based on quantum A∞ algebras.
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This work was supported in part by JSPS KAKENHI Grant Number JP17K05408.
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Okawa, Y. Correlation functions of scalar field theories from homotopy algebras. J. High Energ. Phys. 2024, 40 (2024). https://doi.org/10.1007/JHEP05(2024)040
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DOI: https://doi.org/10.1007/JHEP05(2024)040