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Gravitons are supposed to be the quanta of gravitational field

My question is, if we do not know how to quantize gravity yet, how do we know that quantizing it in principle should give us gravitons, what guarantees that? Why it is always mentioned that gravitons are the gravity force mediators, although we have not quantized gravity yet.

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I know very little of the topic so I won't answer, but the definition of quantizing a theory is to introduce quanta,i.e., particles as excitations of a field. We just call these particles gravitons. –  JeffDror Mar 10 at 9:09

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Associating a particle with a classical field is what quantization does, practically by definition. Take a classical field, make it an operator, and find the eigenstates of its Hamiltonian. The result is particle states, whatever form the field takes. "Graviton" is just the name we give those hypothetical particles.

Even though it's basically just a placeholder name, we can deduce a few properties the graviton ought to have from the general features of quantization. The metric tensor of general relativity is a rank-2 tensor which tells us immediately that the field quantum would have to be a spin-2 particle. The argument is the same as that which tells us that a scalar field has spin-0 particles associated with it, a spinor field has spin-1/2 particles, etc., and is completely general with respect to the form of the field. Also, the metric tensor has a gauge symmetry, which would make the graviton a gauge boson like the photon. Finally, gravity appears to propagate at the speed of light, and hence a gauge boson mediating it would have to be massless.

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Do you know if there is any hypotetical way of tweaking the spin degrees of freedom and make the graviton a fermion? Are there physical arguments against that? –  NikolajK Mar 10 at 9:20
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@NikolajK. Reducing the spin of graviton would mean making gravitation not a tensor field, but some other field. But from the General Relativity we can see that gravity actually is a tensor field. Gravity cannot be a fermionic field, because fermionic fields cannot form macroscopic fields due to the superselection rules: there cannot be a superposition of various numbers of fermions (which is necessary to form a macroscopic long-range field), because there cannot be more than just 1 fermion in the same state (exclusion principle). –  mpv Mar 10 at 12:15
    
To make the graviton a fermion would be more than a 'tweak'. –  DJBunk Mar 10 at 19:17

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