  Recent developments for BPHZ renormalization performed in configuration space
are reviewed and applied to the model of a scalar quantum field with quartic
self-interaction. An extension of the results regarding the short-distance
expansion and the Zimmermann identity is shown for a normal product, which is
quadratic in the field operator. The realization of the equation of motion is
computed for the interacting field and the relation to parametric differential
equations is indicated.
