# A Interpretation of the Weinberg-Witten theorem

1. May 30, 2017

### Afonso Campos

The Weinberg-Witten theorem (https://en.wikipedia.org/wiki/Weinberg–Witten_theorem) states that

A $3 + 1$D QFT quantum field theory with a conserved $4$-vector current $J^\mu$ which is Poincaré covariant does not admit massless particles with helicity $|h| > 1/2$.

A $3 + 1$D QFT with a conserved stress–energy tensor $T^{\mu \nu}$ which is Poincaré covariant does not admit massless particles with helicity $|h| > 1$.

This theorem is interpreted to mean that the graviton cannot be a composite particle. However, I do not quite follow this interpretation.

My understanding is that the massless graviton of spin $2$ ought to have a Poincare-covariant conserved stress-tensor (and Poincare-covariant conserved $4$-vector currents associated to other symmetries). So the Weinberg-Witten theorem means the graviton is not allowed to exist at all.

That the graviton is not allowed to be a composite particle appears to be a weaker conclusion.

2. May 30, 2017

### atyy

3. May 30, 2017

### kodama

4. May 30, 2017

### atyy

The original paper states exceptions, eg. Sakharov gravity.

5. May 30, 2017

### kodama

does WW rule out the possibility gravitons are not fundamental but emergent quasiparticles?

6. May 30, 2017

### atyy

Yes, under the conditions of the theorem. For example, string theory is able to have gravitons that are not fundamental,but are emergent quasiparticles.

7. May 30, 2017

### kodama

what's the difference between a classical graviton and the quantum graviton?

aren't all gravitons quantum bosons?

8. Jun 4, 2017

### tom.stoer

The perspective of the theorem is a graviton on flat, classical Minkowski background with Poincare symmetry, i.e. perturbative gravity. This approach has many other issues, especially perturbative non-renormalizability.

In quantum gravity I would not introduce any background but quantize spacetime as a whole. So there is no background, no QFT on this background and no Poincare invariance at all, which means that the theorem does not apply. In many theories like strings, loop quantum gravity, geometrodynamics with asymptotic safety there isn't even the idea of a fundamental or perturbative graviton, which means the theorem is pointless. It does not affect any theory on quantum gravity I am aware of (the situation nay have been different in 1980)

9. Jun 4, 2017

### kodama

In QM there is the wave-particule duality. Since there are gravitational waves, what is the corresponding particle via duality in quantize spacetime , loop quantum gravity, geometrodynamics

10. Jun 5, 2017

### tom.stoer

Why is there wave-particle duality in quantum gravity? How shall we know? Why is it the correct way to quantize gravitational waves to get gravitons?

Quantizing water waves does not result in H20 molecules, either.

From all what we know it could be the other way round.

In starting with gravitational waves is not like string theory works; gravitons are approximations in a certain regime; background spacetime is restricted to be Ricci-flat, not to be Minkowskian. From asymptotic safety we know that quantizing perturbative gravitons is wrong, whereas an UV completion might be possible but not with the usual perturbative Graviton / not with a Gaussian fixed Point. In LQG there are no Gravitons at all, but it's possible to derive an approximation with an IR graviton propagator.

That means in neither theory Poincare invariance relevant - as far as I can see.

11. Jun 5, 2017

### kodama

quantizing sound waves gives rise to phonons. i have wondered if gravitons are not a fundamental particle but an emergent particle like phonons and how this would affect physics. so the only fundamental bosons are spin0 and spin1

12. Jun 5, 2017

### tom.stoer

Yes, but there are two main differences: phonons are well-defined mathematically (when respecting the lattice cut-off), and they do work in practice, whereas perturbative gravitons neither result in a well-defined theory, nor are required by observations.

I am no so sure what this could mean. Looking at LQG there is nothing like a particle at all. Looking at the asymptotic safety scenario there is a spin-2 field in the path integral, but no perturbative graviton. So somehow QG seems to be very different from QFT.

13. Jun 5, 2017

### kodama

perhaps gravitons need to be defined in terms of a lattice cut-off. ?

Rovelli though did compute 2-graviton for LQG.

any chance you can take a look at this?

Einstein Equation from Covariant Loop Quantum Gravity and Semiclassical Continuum Limit
Muxin Han
(Submitted on 25 May 2017)
In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spinfoam formulation, and how to take advantage of it.

https://arxiv.org/abs/1705.09030

does the paper succeed in its stated aims?

Last edited: Jun 5, 2017