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By renormalization, we have renormalized quantum field theory, usually, we call the theory by effective QFT. What does effective quantum field theory mean? It means we have different quantum field theories that are effective in different case? Or we cann't have unified quantum field theory?

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In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics.

Italics mine.

QFT can be used to model quantum mechanical effects. In that sense there are many quantum field theories.

There is the elementary particle standard model quantum field theory. There are other field theories, as for condensed matter. Back in 1961 I was taught a quantum field theory for nuclear physics, and here is a link called "effective field theory in nuclear physics" .

The "effective" for a field theoretical model means that re-normalization is not a proven effect in the theory. Because the theory fits the data and is predictive in a certain phase space, the problem of renormalization is put under the rug and the theory is used with the title "effective". A prominent example is the use of an effective gravitational field theory in cosmological models, an example.

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  • $\begingroup$ " here is a link called "eefective" nuclear field theory", should be " here is a link called "efective" nuclear field theory ." $\endgroup$ Sep 20, 2022 at 8:24
  • $\begingroup$ Actually, it is not a mathematical tool, in fact, those procedures are not legal. So, I think there is an underlying theory, but we can not hold or get it by modern mathematics, but renormalize to get partial theory or different theory to predict the physical reality. We have not accessed to the unified theory. $\endgroup$ Sep 20, 2022 at 8:30

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