# Feynman rules (vertecies) for graviton

Neitrino
Hi,

Could u advise me please some references where the Feynman rules for graviton are derived I mean graviton-scalar graviton-graviton scattering ... in general graviton vertecies ...

Thank you

## Answers and Replies

Mentor
Such rules would come from a theory of quantum gravity, and we don't have such a (generally accepted) theory yet, as far as I know.

humanino
I formally agree with jtbell, in the following manner : we do not know whether there is a graviton out there, so we can not calculate its "true" Feynman rules. However, I think this is not a very helpful observation.

The graviton is a well defined concept in perturbative quantum general relativity, which although non renormalizable, offers perfectly good effective calculations at low to moderate energies. The results we obtain in the low energy effective theory will be the same as whatever correct UV complete theory would give, in the low energy of course. In this well defined theory, we can in principle calculate the Feynman rules as we please. In practice this is hard. However, we can use insights from even other approaches to quantum gravity, such a string theory, use their mathematical technics in a different physical context. This is done for instance in
Calculation of Graviton Scattering Amplitudes using String-Based Methods
MHV-Vertices for Gravity Amplitudes
Perturbative Gravity and Twistor Space

Note that, they is not easy reading. I would recommend to start with
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
Perturbative Quantum Gravity and its Relation to Gauge Theory

Mentor
OK, I gladly stand corrected!

Neitrino
Thanks Gents ...

schieghoven
Some classic papers.... might be helpful....

Weinberg's computation of `gravitational bremsstrahlung': should give you the lepton-graviton vertex. Excellently written, as ever...
Weinberg, S., Infrared Photons and Gravitons,
Phys. Rev., 1965, 140, B516

Graviton self-coupling, and graviton-scalar.... including proofs that the former is renormalizable at one loop, the latter is not. This is why @humanino refers to treating gravity as an 'effective field theory'.
't Hooft, G., One-Loop Divergencies in the Theory of Gravitation,
Ann. Inst. Henri Poincare A, 1974, 20, 69-94

Graviton-lepton again, same conclusion...
Deser, S. & van Nieuwenhuizen, P., Nonrenormalizability of the quantized Dirac-Einstein system,
Phys. Rev. D, 1974, 10, 411-420

Cheers,

Dave

mike372
These were calculated for KK gravitons in large extra dimensions in arXiv:hep-ph/9811350 . For normal gravitons just use the zero mode solutions.

jfy4
A frankly adorable exercise is to quantized the Linearized Einstein field equations in the Lorentz Gauge.

$$\mathbf{\Box} g_{\alpha\beta}=0$$

This actually provides some insight into quantum gravity, just as the low energy limit quantization does.