I'm wondering why correlation function is a more fundamental object in conformal field theory than the notion of particle. By conformal symmetry, I think we can still discuss about massless particle.
I'm wondering if there will be bound state and scattering state, those exists in quantum mechanics scattering theory, will they still work in CFT?
Also, I'm wondering why don't we draw Feynman diagram in CFT and why CFT don't have Lagrangian?
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2The notion of particles and correlation functions are not mutually exclusive. Also, CFTs can have Lagrangians, indeed the first example one encounters is usually a mass less scalar. – JamalS Jul 01 '20 at 12:44
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1Some CFTs have Lagrangians, some don't. Not needing to work with a Lagrangian is part of the power of CFT. – 4xion Jul 02 '20 at 02:16
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correlation functions are fundamental in QFT too, but here's an old post on particles in CFT: https://physics.stackexchange.com/questions/78552/why-are-there-no-particles-in-conformal-theories – 4xion Jul 02 '20 at 02:18