# Graviton Propagator and energy-momentum tensor

• Neitrino
In summary, the conversation discusses the coupling of graviton propagator with the energy-momentum tensor of matter fields and its implications on the conservation of energy-momentum and the propagator's contribution in different scenarios. It also mentions the presence of terms in the propagator that do not depend on momentum, leading to the Newtonian potential in the nonrelativistic limit.
Neitrino
Dear PF,
I am a little bit confused could you pls help me ...

Suppose I a have a scatering or conversion of two particles via graviton propagator.
Graviton propagator couples with energy-momentum tensor of matter fields.

So can i assume that vertex to which graviton propagator is coupled is in fact energy-momentum tensor ?

Energy-momentum tensor is conserved and thus if i take graviton propagator in some general case where i have graviton momentum in numerator it should give me vanishing contribution.

But energy-momentum tensor (which I cast in this case as a vertxe +external lines) contains two different momentum: ingoing momentum p1 and ingoing momentum p2, so my propagator momentum will be q=p1+p2... so does it mean that when I express graviton momentum through p1+p2 and and couple it to a vertxe i will have identical zero...?

Thanks

There are terms in the graviton propagator that do not have factors of the momentum in the numerator. For example, in harmonic gauge

$$D_{\mu\nu,\rho\sigma} = \frac{1}{q^2} \left( \eta_{\mu\rho}\eta_{\nu\sigma} + \eta_{\mu\sigma}\eta_{\nu\rho} - \eta_{\mu\nu}\eta_{\sigma\rho} \right).$$

This expression leads to the Newtonian potential in the nonrelativistic limit, as outlined for example, in section 4 of http://arxiv.org/abs/gr-qc/9512024.

## 1. What is the Graviton Propagator?

The Graviton Propagator is a mathematical construct used in quantum field theory to describe how the force of gravity is transmitted between particles. It represents the probability amplitude for a graviton, the hypothetical particle that carries the force of gravity, to travel from one point in space to another.

## 2. How is the energy-momentum tensor related to the Graviton Propagator?

The energy-momentum tensor is a mathematical object that describes the distribution of energy and momentum in a given region of space. In the context of general relativity, it is also related to the curvature of spacetime. The Graviton Propagator is derived from the energy-momentum tensor, as it represents the interaction between particles due to the curvature of spacetime.

## 3. What is the significance of the Graviton Propagator in physics?

The Graviton Propagator is a key component in the field of quantum gravity, which aims to unify the theories of quantum mechanics and general relativity. It helps explain how gravity, which is described by general relativity as a curvature of spacetime, can also be described by a force-carrying particle, the graviton, in quantum mechanics.

## 4. How is the Graviton Propagator calculated?

The Graviton Propagator is calculated using Feynman diagrams, which are graphical representations of mathematical equations that describe the interactions between particles. These diagrams involve complex integrals and calculations, and are used to calculate the probability amplitudes of various interactions, including the propagation of gravitons.

## 5. Can the Graviton Propagator be experimentally measured?

Currently, the Graviton Propagator has not been directly measured in experiments. This is due to the extremely small scale at which gravitational interactions occur and the difficulty in detecting gravitons. However, there are ongoing efforts to indirectly measure the effects of gravitons and further test the predictions of quantum gravity theories.

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