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I know some aspects such as the extra dimensions have been used in String Theory, but is it possible to make a Quantum Field Theory out of Kaluza-Klein Theory, and how does it differ from Quantum Gravity as an effective field theory & Quantum Electrodynamics?

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is it possible to make a Quantum Field Theory out of Kaluza-Klein Theory,

Yes, at least as an effective field theory, with a cutoff scale given by the Planck mass associated with the higher dimension.

See, eg, slides 117 and 118 here: https://indico.cern.ch/event/575526/contributions/2368967/attachments/1430033/2196226/Mondragon_BeyondSM_L3.pdf

and how does it differ from Quantum Gravity as an effective field theory

Kaluza-Klein theory can be viewed as an effective field theory of quantum gravity with compact dimensions. It differs from an effective field theory of gravity in 4 space-time dimensions because of the extra compact dimensions (sorry this is a sort of tautological answer, but you asked). In more detail, Kaluza-Klein gravity contains additional massless states relative to pure gravity (if you compactify 1 extra spatial dimension, you get a U(1) field and a scalar field called the dilaton describing the size of the extra dimension), plus an infinite tower of massive states.

& Quantum Electrodynamics?

QED does not contain a dynamical metric, a dilaton (or other moduli fields) associated with the compactified extra dimension, or a tower of massive states.

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