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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

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- Thread starter Neitrino
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- #1

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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

- #2

jtbell

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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

- #4

jtbell

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OK, I gladly stand corrected!

- #5

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Thanks Gents ...

- #6

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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

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- #8

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[tex]\mathbf{\Box} g_{\alpha\beta}=0[/tex]

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

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