Correlation functions involving Dirac fields from homotopy algebras II: the interacting theory

We extend the formula for correlation functions of free scalar field theories and Dirac field theories in terms of quantum $A_{\mathrm{\infty }}$ algebras presented in arXiv:2305.11634 to general scalar-Dirac systems. We obtain the result that the same formula as in the previous paper holds in this case. We show that correlation functions from our formula satisfy the Schwinger-Dyson equations. We therefore confirm that correlation functions from our formula express correlation functions from the ordinary approach of quantum field theory.