  Well-defined nonlinear deformations of free quantum fields are introduced as
manifestly Poincar\'e invariant scaling and resonance properties of
non-dynamical scale models in Minkowski space, instead of introducing nonlinear
dynamical deformations of free quantum fields that require the various
truncations and scaling corrections of regularization and renormalization. With
the given algebraic construction, energy and momentum operators can be
constructed \emph{ex post facto} as the generators of translations. A weakened
version of microcausality emerges naturally, "convex hull microcausality"
---that operators associated with two regions of space--time must commute if
\emph{the convex hulls of} those regions are space-like separated---, which is
enough for us to be able to construct an abundant class of interacting quantum
fields.
