Correlation functions of scalar field theories from homotopy algebras

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 ${\phi }^3$ 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.

arXiv comment35 pages, 3 figures; v2: minor changes; v3: the paragraph below (2.17) added, (2.64) added, the explanation below (4.37) added, and the fourth paragraph of section 7 added, version published in JHEP

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Cited by in corpus (4)

• Nonperturbative correlation functions from homotopy algebras
• Correlation Functions Involving Dirac Fields from Homotopy Algebras I: The Free Theory
• Correlation functions involving Dirac fields from homotopy algebras II: the interacting theory
• Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude