Not included in this blog but required is some knowledge of thermodynamics and contour integration. Just to give a perspective on this topic, twenty years ago, EFT was found in some section of a chapter in QFT. Today, in some universities, you will find a full semester course on this subject, a testimony of how much in importance EFT has grown. In this blog I show that a quantum effective field = a classical field + 1st order quantum correction. More generally, any theory A in high energy can be broken down to a theory B in lower energy plus some correction orders. For instance, not knowing a quantum gravity theory at Planck scale ( 1019GeV) still allows us to do QFT at lower energy ( LHC at 103GeV).

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