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I am curious about the following and I aim these questions to the people who do general relativity and uantum field theory over there.

What is the difference between field theory of general relativity and field theory of quantum field theory? Is the former only for study of gravitation while the latter covers broader scope, including quantum theory of gravitation?

Are mathematics subjects like differential geometry, manifold, topology and the likes are that needed and useful for quantum field theory (while to my knowledge these mathematics are mandatory to study GR)?

In particular, do condensed matter theorists indeed need these mathematics to study high level and rather abstract "types" of condensed matter physics like fractional statistics, anyon, fractional quantum Hall effects,etc?

I am quite surprised to hear that many people say that quantum field theory unifies relativity and quantum mechanics, but which relativity? If it is the special one, then I guess quantum field theorists need no bother about general relativity, which I can't believe!!!

Conversely, since general relativity, if I'm not mistaken, is still classical physics stuff, then experts on these need not deal with quantum field theory (since the former deals more with theory of space of time in gravitation than field theory in general as the latter does)???

Please enlighten me. Thanks.

regards

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# General relativity vs quantum field theory

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