Intuitive method for constructing effective field theories

We derive a novel method for constructing effective field theories. Physically, the method is very close to the intuition behind effective field theories: One can integrate out the heavier scale directly from the path integral. We give a detailed recipe for the effective field theory construction, which is nearly identical to the construction of the so-called 1PI effective action. We also demonstrate the equivalence of the novel method to the commonly used procedure of matching Green's functions.