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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.

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    $\begingroup$ 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. $\endgroup$ – Luboš Motl Jun 23 '14 at 17:38
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    $\begingroup$ @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. $\endgroup$ – TwoBs Jun 24 '14 at 8:38
  • $\begingroup$ @TwoBs Could you clarify EFT and UV? I am unfamiliar with those acronyms. $\endgroup$ – Ethan Reesor Jun 24 '14 at 16:04
  • $\begingroup$ EFT: Effective field theory - an approximation for low energies. UV: ultraviolet - the high-energy regime. $\endgroup$ – Robin Ekman Jun 24 '14 at 16:35
  • $\begingroup$ @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. $\endgroup$ – TwoBs Jun 24 '14 at 19:54
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The answer to the question is yes. The framework of quantum field theory allows one to describe all interactions except for gravity. Different realizations of QFT take account for different fields of physics: For example, phenomena of electromagnetism are described accurately by quantum electrodynamics, while the strong interaction that describes how nuclei behave is covered by quantum chromodynamics. Together with the theory of weak interactions, these two theories form the Standard Model of Particle Physics. Apart from particle physics, there also exist quantum field theoretic approaches towards condensed matter physics.

The problem with a fundamental quantum field theory of gravity is that when one naively starts from general relativity and tries to quantize it, one runs into the difficulty of nonrenormalizability. This means that one encounters divergent integrals that cannot be removed by modifying the theory, making the theory useless. One solution to this problem may be approaching the issue from a different perspective and use the framework of string theory.

The reason why quantum field theory is successful is the fact that at high energies and small distances, nature is dominated by both relativistic and quantum mechanical effects, and quantum field theory can be seen as a unification of special relativity and quantum mechanics.

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A quick clarification: quantum field theory is a classification of theories, that is there can be many different quantum field theories. The Standard Model is an example of a quantum field theory, and it does indeed describe all the phenomena we know about except for gravity. You might be interested to read this summary of the current (well, current as of 18 years ago) status of field theory by David Gross.

Although the Standard Model does not include gravity there is a different quantum field theory called N=8 Supergravity that does attempt to describe gravity. In the past I have seen arguments about whether or not the theory could work - it's too far beyond what I know for me to express an opinion.

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