The redshift can be described by quantum field theory on a curved background.  This is not a quantum theory of gravity, because the gravitational field is described by classical equations.  As a theory it would not be self-consistent, but as an approximation it seems quite adequate. 

For the redshift in a classical gravitational field, the theory is certainly sufficient.

Dr. Schmelzer, thank you for your answer.

Dear Dr. Cornwall, thank you for your answer.

The question is:  What is the level of energy for the photon-graviton interaction?

It is generally thought it is the level of Planck energy. But, it seems that, in the gravitational redshift, the level of energy is much lower.

Dear Yyn Zhu,

Perhaps my answer will be stranger … But I appreciate lot your Country achievements in last 25 years, and existing possibility for verifying some similar Thoughts…

In the last ten years I have  tried to approach to the gravity problems onto base of real phenomena  (Earth’s Gravity field)  after abandoning  the existing gravities models…  The idea was gotten onto base of asteroids of inner asteroid belt… Why they are existing close to the draft planets (like Ceres) and the The Exploded Planet Hypothesis 2000 of Tomas Wan Flanderm (http://www.metaresearch.org/solar%20system/eph/eph2000.asp) It can be gotten a resolution more slowly process in geological scale similar effect like in case of shown theory… The erosion of planets forming asteroid belt and Ceres like dwarf planet…  without contradiction if an exited rocky planet was exploded it would not have possibility existence of Ceres like dwarf planet…    

(The planet erosion theory in the next blog http://planeterosion.blogspot.hu/) (2007)

So has remained a very important question: how can be possible the moving away of fragments from the surface of planet under erosion… Plus existed an calculation using Newtonian formula with the density of Earth and density of Moon… and taking consideration inner structure of Earth and Moon … Getting conclusion… (1) That Earth’s core has approximate 75 g/cm3- only around 2011 I had gotten idea that is impossible when discussed Growing Earth theory of my friend -…( 2 ) Moon  has no tidal influence to Earth!-  without explanation- a…. And Only in 2009 I have gotten the resolution of the gravity problem  (actually the work is exiting here in Hungarian Tittle: Tényekkel Igazolható a gravítáció valos oka- The real cause of gravity can be demonstrated with facts… Now rehome to your questions I am going to respond with next consideration… That The gravitational redshift I will not take in consideration (onto Lao Ce teaching) we are not able to verify… I will take in consideration the Earth’s gravity… It is possible the describing of Earth’s gravity with Quantum mechanics  (onto level  of Plank energy) we can got the best resolution If The Earth Gravity is explained onto base of electrostatics – electrodynamics, and plasma physics  laws…

if a photon hn travels 1m against the gravitational field of the earth it "looses" ~ 10-16 of its energy. No idea whether this is now of order Planck.

Dear Dr. Schober,

Thank you for your answer.

I agree your conclusion.

But, it is generally thought that the level of Planck energy is needed for the photon-graviton interaction.

Dear Dr. Horvath,

Thank you for your answer.

@dear Dr. Yin Zhu. „...it is generally thought …”???. Obviously, is my ansatz not basic photon-gravity? Planck energy is ~ 1028 eV, so such a „photon“ looses/gains ~ 1012 eV in 1m Earth gravity, which is nice, may be visible in astrophysics? Next we take the standard QFT Lagrangian L = ½(E² - B²) ---> H =  ...a+a (obvious notation), add a covariant quartic interaction term (like Higgs) including “potential” –1/r (like strings, here: delta function). Now you may start computing whatsoever. This will keep busy noumerous researches, but it is still standard QFT.

Dear Dr. Schober,

Please reference: Is a graviton detectable?

F Dyson - International Journal of Modern Physics A, 2013

dear Dr. Yin Zhu, to argue with authorities is the one thing ..., but especially here at RG one could/should try to promote his own opinion: "they" detect gravitons/gravitational waves since decades, unfortunately later it turnes out, something went wrong during collecting data. Quantum theory was developed by the evidence of nonclassical data, called quantum effects. Tell me, what is the need to develope a "quantum gravity"? On the other hand, there are noumerous ways out of the "dilemma": make the gravitons "confined" like quarks, let them "oscillate" into further unknown states ("new" supersymmetry or dark matter) or escape into dimensions beyond the twenty string-ones, ... . Now to your question: Is a graviton detectable?, This is a matter of taste: Yes, If the scientific community (these "authorities" of course) agree it is  detected, Exactly this happened last year at CERN, they "detected"  the Higgs, better: god's particle. May be they detected a machine resonance of this LHD and I'm sure next they "detect" supersymmetry. But, remember, first they should "detect" gravitational waves! Till today: nothing: Who cares? Lets jump to the graviton.

Anton, the need for quantum gravity follows from the belief that there exists a single consistent theory which describes everything.  This theory would have to describe quantum effects as well as gravity.  

If you think that there are various ways out, feel free to develop one.  The graviton will be, of course, extremely difficult, close to impossible, to observe.  But so what?  There should be at least a consistent theory which describes quantum effects as well as gravity - if with or without gravitons is irrelevant, but it seems extremely plausible that it has to be with gravitons.  

You have to believe quite a lot: as a matter of facts most of the baryons below the upsilon cannot be squeezed into SU(3) multiplets. Next, leptonic SU(2) multiplets do not exist at all: But you start with SU(3)xSU(2)xU(1) as basic setting, and for the passage to SU(5) you need this "running coupling constant" which has to be a Lorentz scalar but it is'nt. So, this theory is not covariant, forget it. Anyway, non existing proton decay is ignored, and beyond this we have the great desert. We cross this with our escort susygut. Why should we unify the coupling down to gravitational coupling constant. Why stop there? I would scale it down to zero, and this theory we finally understand: only free particles.

 Dear Yin Zhu,

   I'm probably the wrong person to ask; I have rather unconventional ideas about the need for quantum gravity.  However, I think your question about gravitational redshift is a little premature before one has a quantum theory of gravity.  Quantum electrodynamics takes place in Minkowski space.  The analog in general relativity is a freely falling frame in which there is no gravtational force,  Einstein's view is that a direct gravitational force is an illusion caused by being in an accelerated frame of reference.  Looked at in this way, gravitational redshift is a kinematic effect of being in a non-inertial frame.  It's the same whether you are in a gravitational field as it is in an accelerated elevator.  The real gravitational force, e.g., as in gravitational waves (gravitons), are tidal forces which are peripheral to gravitation redshift.  Although I'm not an expert, I suspect that one of the problems of quantizing gravity is how to deal with the lack of a global Lorentz frame.  Even when (if) gravity is quantized, it's quite possible that gravitational redshift will still be best described as a kinematic effect in a non-intertial frame of reference; however, like I say, I'm not an expert in quantum gravity.

Dear Dr. Schober and Dr. Schmelzer,

Several papers researched the photon-graviton interaction. I think, a real photon-graviton interaction may be observed in the gravitational redshift. Then, what shall happen as the gravitational redshift is described with photon-graviton interaction?

This is why I have this question.

Dear Dr. Boughn, thank you for your answer.

Dear Yin Yhu,

We have gotten very plausible answer from Dr, Anon Schober to your question... I am only partially inside in the subject, because *authorities* communicates a theoretical science lot of time no concordant with reality (gravity theory, planetary system formations, plate tectonics...)... reading your sentence- I think, a real photon-graviton interaction may be observed in the gravitational redshift. - How we can count with a particle, graviton which existence did not be demonstrated yet... Onto base of my own beliefe, i think the existence of gravion never will be demonstrated, because graviton existence totally contradict our observable surroundings mechanism... If exist graviton we cannot get medium like where we are living... A particle with only gravitation result  a  system where this particle will evolve with continuu evolution... example only In Black Hole... That is a deep contradiction...

...The light behavior like a particle (photon) is demonstrated, so these photon may have gravitational fields which are in continue variation function with the medium where the light moves..

There is the

Take the example o fDr, Anon Schober- if a photon hn travels 1m against the gravitational field of the earth it "looses" ~ 10-16 of its energy.- What is your opinion what will happen with this energy looses.... 

Dear László-Attila Horváth, you made the point: what is the difference of a photon loosing energy in a Coulomb field or in a gravitational field? The QFT interaction term is qAj. Red shift is the same, interaction term should be the same (=similar)

Dear Anton Schober… Thank you!

“What is the difference of a photon loosing energy in a Coulomb field or in a gravitational field?”- My answer same (similar)…  There is the response to your Question Dear Yin Zhu… The quantum field theory can be used to describe the gravitational redshift… with a theory where exist (something  equivalence ?) between Gravity field and Coulomb field… Perhaps such a theory does not accepted by authorities… because at them the Gravity field does have same  source like Coulomb field…. But in reality exist such a material stage which produce gravity Field (Our Earth outer core ) No bary centre and no time-space curvature… Example exist clear evidence that the Earth tides is not caused by the gravity field of Moon!... Galileo had a better explanation to Earth Tides like Newton…  http://galileo.rice.edu/sci/observations/tides.html ...And if the theory of gravitation evolved in direction which taking in consideration Galileo thinking we would have such a theory where Coulomb field has (something equivalence?) with gravity field…

Dear Dr.  Schober and Dr. Horváth,

Thank you for your comments. It is sure, " Perhaps such a theory does not accepted by authorities".

I have a paper "Graviton-photon interaction in the gravitational redshift"

https://www.researchgate.net/publication/278111169_Graviton-photon_interaction_in_the_gravitational_redshift

If you should have any comments on it, I should thank you very much.

Research Graviton-photon interaction in the gravitational redshift

Your graph in fig.2 says: the sum of four light-like 4-vectors is zero. We know, there is no photon-photon interaction, so you replace 2 photons by "gravitons".  You say nothing how this interaction works, so you should assume pointlike interaction like low energy beta decay: (n;p,e,nu). next, how about photon- graviton coupling strenght? Compute this! the energy loss by redshift is known. good luck!

Dear Dr. Schober, thank you for your comments.

1, It is a good question: "how about photon- graviton coupling strenght?"

2, Now, it has been known that there is photon-photon interaction. Please see Ref. 8.

for ref 8 I need a link here. However, ..  in a quantum nonlinear medium (!?). How about in the vacuum?

Dear Dr. Schober,

This is the link

http://www.nature.com/nature/journal/v502/n7469/abs/nature12512.html

very funny: 

Purchase article full text and PDF: €30

This question was discussed here in this RG https://www.researchgate.net/post/The_gravitational_redshift_is_a_phenomenon_based_on_gravitational_time_dilation_dont_we_want_to_exclude_definitely_any_loss_of_energy_of_photons

I think we have reached to the answer!! In fact there is no graviton, it is only photon!!! To understand more about that review my paper http://vixra.org/abs/1509.0059

Dear Dr. Almosallami,

I do not think there is the so-called Einstein's gravitational time dilation.

It is absolutely  clear and certain, the effect of the Newtonian gravitational force on the atomic clock on the level of (altitude) 1cm  is easily measured. While, as some one claimed, the effect of the  so-called Einstein's gravitational time dilation can only be observed on the level higher than 15cm can be observed.

But, in the experiment claimed to prove the so-called Einstein's gravitational time dilation, the Newtonian gravitational time effect has not been measured.

Please reference:

Is the Hafele-keating experiment credible?

https://www.researchgate.net/post/Is_the_Hafele-keating_experiment_credible

Dear Andrew Wutke,

The next discussions are also useful the next to the before made comment:

https://www.researchgate.net/post/Can_Maxwell_equations_apply_to_gravity#view=575d1f3b404854f03305b561

https://www.researchgate.net/post/How_to_describe_the_gravitational_redshift_with_the_quantum_field_theory/2

https://www.researchgate.net/post/How_to_describe_the_gravitational_redshift_with_the_quantum_field_theory

Ordinary quantum field theories are based on gauge invariance and Lorentz invariance. It is not a class of theories addressing gravitational interactions. Gravitational effects at the quantum level are addressed by quantum gravity. Instead of using quantum field theory, it is possible to use very basic physical arguments to explain gravitational redshift, see for example,

http://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch07Rel.pdf