General relativity, Electromagnetism and Feynman Diagrams

[LCSphysicist]

TL;DR Summary

Currently I am re-reading Sean Carrol, general relativity. But a thing got me stuck in, I can't understand what he is talking about.

We are discussing the introduction to Einstein field equation, so he start talk about the linearity in Newtonian gravity and the non linearity in GR. But there is somethings I am missing:

> " (...) in GR the gravitational field couples to itself (...) A nice way to think about this is provided by Feynman diagrams (...) There is no diagram in which two photons exchange another photons between themselves, because electromagnetism is linear."

Particularly, I can't understand these citations.

First I am not sure what means a field to couples to itself, but I think it means it is linearity so the field in a point add linearity.

And I couldn't understand how does the fact that that the electromagnetism is linear imply that photons do not exchange photons between, I can see these both statements are right, but can't see the connection between them, so that one implies the other.

 

[PeterDonis]

I am not sure what means a field to couples to itself, but I think it means it is linearity

No, it means nonlinearity. A linear field has no self-coupling. A nonlinear field does have self-coupling.

I couldn't understand how does the fact that that the electromagnetism is linear imply that photons do not exchange photons

Because if the field equation is linear, as Maxwell's Equations are, then the corresponding quantum field theory has no self-coupling term (because such a term would have two factors of the field, so it wouldn't be linear in the field), so there is no photon-photon coupling term in quantum electrodynamics.

The Einstein Field Equation, however, is nonlinear, so the corresponding QFT would have a self-coupling term.

More details in this series of Insights articles (the link is to the first of 3):

https://www.physicsforums.com/insights/does-gravity-gravitate/