Effective field theory and classical equations of motion

Given a theory containing both heavy and light fields (the UV theory), standard procedure is to integrate out the field obtain an effective (EFT) for fields. Typically, EFT equations of motion consist expansion involving higher derivatives fields, whose truncation at any finite order may not be well-posed. In this paper, we address question how make sense whether they provide good approximation classical theory. We propose approach solving EFTs, which leads well-posedness statement. For particular choice theory, rigorously derive corresponding show that large class solutions are well approximated by solutions. also consider solutions, demonstrate these close, in averaged sense, modified EFT.