  We derive the new identity in homotopy algebras which directly corresponds to
the Schwinger-Dyson equations in quantum field theory. As an application, we
derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi
identities are reproduced in several examples. In general, our formula contains
divergence. We mediate this problem by introducing stubs known in the context
of string field theory. With the regularization, we can calculate the anomaly
such as axial U(1) anomaly in vector-like U(1) gauge theory.
