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Consider the action $$\int \sqrt{-g}\left[R[g]+\mathcal{L}_{m1}(g,\psi_1)+\mathcal{L}_{m2}(g,\psi_2)\right]$$ Classically we have $$\nabla^\mu T^1{}_{\mu\nu}=0,\,\,\,\,\nabla^\mu T^2{}_{\mu\nu}=0$$ seperately. Point is that at the level of classical action $\psi_1,\psi_2$ does NOT interact directly but they both interact with gravity, that is to say, there are no terms of the form $\mathcal{L}_{int}(g,\psi_1,\psi_2)$, which, if present, would enable the two sectors to covariantly exchange energy-momentum and reduce the relation above to the weaker form $$\nabla^\mu(T^1{}_{\mu\nu}+T^2{}_{\mu\nu})=0$$

My question is whether quantum corrections can have such effects as well? Because naively it seems quantum mechanically many possible direct interaction terms between $\psi_1$ and $\psi_2$, even if no such terms are present in the classical action.

Thanks a lot!

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  • $\begingroup$ Is there anyone? $\endgroup$ Dec 8, 2014 at 14:46
  • $\begingroup$ Is this question too trivial to answer? Sorry I am not very good at quantum fields $\endgroup$ Dec 8, 2014 at 14:47
  • $\begingroup$ Well, it has been viewed 22 times by now, and none of us seem to want to undertake an answer. My answer would be hand waving :gravitation and quantum mechanics become in numbers commensurate at the very high densities and energies in the beginning of the Big Bang. For usual environments even if there, the terms would be so small as to be ignored. $\endgroup$
    – anna v
    Dec 11, 2014 at 5:20

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