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Recent developments for BPHZ renormalization performed in configuration spaceare reviewed and applied to the model of a scalar quantum field with quarticself-interaction. An extension of the results regarding the short-distanceexpansion and the Zimmermann identity is shown for a normal product, which isquadratic in the field operator. The realization of the equation of motion iscomputed for the interacting field and the relation to parametric differentialequations is indicated.

BPHZ Renormalization in Configuration Space for the $\mathcal{A}^4$-Model