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arXiv · 2203.05366

Correlation functions of scalar field theories from homotopy algebras

Yuji Okawa
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Abstract

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 $\varphi^3$ 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.

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Yuji Okawa. 2022-03-10. Correlation functions of scalar field theories from homotopy algebras. https://doi.org/10.1007/jhep05(2024)040

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