  We develop the idea that renormalization, decoupling of heavy particle
effects from low energy physics and the construction of effective field
theories are intimately linked to the momentum space entanglement of disparate
modes of an interacting quantum field theory. Using unitary transformations to
decouple these modes at the perturbative level, we show in a scalar field
theoretical model with light and heavy fields, how renormalization may be
consistently implemented and how the low energy effective field theory can be
constructed. We also obtain a renormalization group equation in this framework
and apply it to the scalar field theoretical model.
