An effective field theory describes phenomena below a chosen energy scale by retaining the relevant light fields and organizing local interactions by increasing suppression at that scale.
Integrating out a field means performing its path integral while retaining the other fields as backgrounds. The result is generally a nonlocal quantum effective action; for a field much heavier than all external momenta, a derivative expansion turns it into local effective interactions.
A derivative expansion expresses a nonlocal effective interaction as a series of local operators with successively more derivatives. For a field of mass , each additional pair of derivatives is typically suppressed by .
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Effective field theory (EFT) is a framework in theoretical physics used to describe physical systems at specific energy scales while accounting for the effects of higher energy processes in a systematic way. The main idea behind EFT is that, at a given energy scale, we can ignore the details of physics that occurs at much higher energy scales, focusing instead on the degrees of freedom and interactions relevant to the low-energy behavior of the system.
www.youtube.com/watch?v=WB8r7CU7clk&list=PLUl4u3cNGP60TvpbO5toEWC8y8w51dtvm by Iain Stewart. Basically starts by explaining how quantum field theory is so generic that it is hard to get any numerical results out of it :-)