  Quantum scale invariant regularization is a variant of dimensional
regularization where the renormalization scale is treated as a dynamical field.
But, rather than be regarded as a novel regularization method on par with
dimensional regularization, momentum cutoff, Pauli-Villars etc., it should be
understood as a way to define a subset in the infinite space of
nonrenormalizable models of certain type. The subset realizes the demand that
renormalization scale, along with any other dimensionful parameters, should be
interpreted as a dynamical field's homogeneous background. This restriction is
most straightforwardly implemented using dimensional regularization but it can
hypothetically be imposed with any regularization method. Theories that satisfy
it offer a new perspective on the radiative violation of global scale symmetry
associated with RGE functions. As a result of the quantum scale invariant
regularization being implemented, the scale symmetry is preserved at the
quantum level despite the RGE functions being non-zero, as can be inspected at
the level of composite quantum operators that govern dilatation of Green
functions. We analyze these statements in explicit detail using a specific but
easily generalized toy model with scalar fields.

High Energy Physics - Theory