# Graviton Model: Can We Describe It Mathematically?

• A
• alantheastronomer
Higgs boson).In summary, in the 1960s and early 1970s, a quantum field theory of a massless spin-2 field was developed as an analogy to the QFT of the massless spin-1 field. However, this theory is not renormalizable and there is no experimental evidence for the existence of gravitons. There is also no known relationship between the graviton and the Higgs boson, and it is not clear whether gravity is fundamental or emergent.f

#### alantheastronomer

We know that the photon is the quanta associated with the electromagnetic field; and we've successfully observed gravitational waves due to LIGO. Is there any corresponding theoretical mathematical description of the graviton?

Is there any corresponding theoretical mathematical description of the graviton?

In the 1960s and early 1970s, a quantum field theory of a massless spin-2 field was developed, analogous to the QFT of the massless spin-1 field (electromagnetic field). There is some discussion of this in this previous PF thread (see also the paper by Deser linked to in one of my posts in that thread):

Great, thanks!

To add: it's called Fierz-Pauli theory. See e.g. Hinterbilcher's notes on massive gravity at the arXiv.

In the 1960s and early 1970s, a quantum field theory of a massless spin-2 field was developed, analogous to the QFT of the massless spin-1 field (electromagnetic field). There is some discussion of this in this previous PF thread (see also the paper by Deser linked to in one of my posts in that thread):

Ok, so my takeaway from this thread is that; since the gravitational field is non-linear the graviton has a self-interaction and because of that causes it to be a non-conserved quantity, which calls it's validity into question. Do I understand that correctly?
Follow up question - The Higgs boson is said to imbue particles with mass, while the graviton is the mediator of the gravitational interaction among masses. So what relationship, if any, is there between the graviton and the Higgs boson?

since the gravitational field is non-linear the graviton has a self-interaction

Yes.

and because of that causes it to be a non-conserved quantity

I don't know what you mean by this.

The Higgs boson is said to imbue particles with mass

With rest mass, yes.

the graviton is the mediator of the gravitational interaction among masses

No, among energies. Energy gravitates whether it takes the form of rest mass or not.

PeterDonis said:
I don't know what you mean by this.
You said in post#12 of the thread you provided; "If we really want the RHS of our equation to represent all of energy present, including the energy due to the graviton field, then we have to rearrange terms in the EFE to put "gravitational energy" on the RHS...
2) However we do it, we lose the property of both sides of the equation having zero covariant divergence; i.e., we lose automatic conservation of the source.
...you can have "energy in the gravitational field" included in the "source" but only at the expense of having the source no longer be automatically conserved."

So, has there been any relationship established between the graviton and the Higgs boson?

you can have "energy in the gravitational field" included in the "source" but only at the expense of having the source no longer be automatically conserved."

Yes. But this has nothing to do with the EFE, the graviton field equation, being nonlinear (i.e., self-interacting). It has to do with the Einstein tensor being the one that satisfies the Bianchi identities. The same kind of phenomenon occurs in electromagnetism, even though the photon field equation--Maxwell's Equations--is linear: the photon field carries no source (charge-current), and this is what enables automatic conservation of the source in the field equation.

You should probably read my series of Insights articles on "does gravity gravitate"? There are a lot of issues here that you don't seem to be aware of. The series starts here:

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

Also, none of this calls the validity of the spin-2 field model into question. The main issue with the quantum field theory of the spin-2 field is that it is not renormalizable (whereas the Standard Model of particle physics, for example, is). But most physicists today believe that none of the QFTs we have today are truly fundamental, so non-renormalizability doesn't make them invalid, period; it just limits the domain in which they are valid (roughly, energies that are small compared with the energy at which the non-renormalizable terms in the Lagrangian become significant).

has there been any relationship established between the graviton and the Higgs boson?

The graviton is not included in the Standard Model, which is the QFT that includes the Higgs boson. So other than the Higgs boson carrying stress-energy, which all of the Standard Model fields do, there is no relationship known.

Also, the spin-2 field theory of the graviton is speculative, since we have no prospect of measuring any quantum aspects of gravity or gravitational waves any time soon so there is no experimental evidence for gravitons.

weirdoguy
We also don't know whether gravity is fundamental or emergent, i.e. whether the hypothetical graviton would be a quasiparticle (like the phonon) or fundamental (like the photon).