# Quantum field theory's completeness

I realize Quantum Field Theory doesn't include gravity at all. Other than that, does QFT completely describe all electromagnetic and nuclear interactions? In other words, does it describe (at least) everything the classical field theories did (other than gravity)?

Do the QFTs of the standard model describe all interactions of those fields? In other words, do QED, QCD, and QFD/EWT describe at least everything their classical counterparts do?

EDIT: The question has not changed; it has been reworded to use the phrase QFT more correctly.

• Yes. All simple enough quantum theories have a classical limit, so the quantum theories may obviously do "everything" that the classical theories did. (The classical theories emerge as a limit of quantum theories.) They just do it more correctly in the quantum regime because everything in Nature is quantum. Jun 23, 2014 at 17:38
• @FireLizzard QFTs can and easily include gravitational low energy phenomena. There is no problem in including the graviton using the Einstein Hilbert action, as long as one restricts itself to finite energy and finite accuracy. In other words, gravity as an EFT is fine. See the very nice discussion in the recent book by Matt Schwartz in sect. 22.4 assets.cambridge.org/97811070/34730/toc/9781107034730_toc.pdf where he shows the universal low energy prediction of quantum gravity. As any EFT, the problem of gravity+QFT is about the bad UV behavior, which is cured by string theory. Jun 24, 2014 at 8:38
• @TwoBs Could you clarify EFT and UV? I am unfamiliar with those acronyms. Jun 24, 2014 at 16:04
• EFT: Effective field theory - an approximation for low energies. UV: ultraviolet - the high-energy regime. Jun 24, 2014 at 16:35
• @FireLizzard EFT is for 'effective field theory'. They are theories which are valid within a certain range of energies. In the case of gravity: the Standard Model+ gravity minimally coupled+ Einstein Hilbert action provides nothing but an effective theory valid for energy much smaller than Planck, $E\ll M_{pl}$. At energy $E$ above $M_{pl}$ the theory breaks down (predicting as it is silly things). But as long as you restrict to $E\ll M_{pl}$, and your experimental accuracy isn't better than one part in $M_{pl}^2/E^2$ you predictions will be very accurate. Jun 24, 2014 at 19:54