# Weinberg-Witten theorem and Landau pseudotensor, or how QFT can make prediction about GR

1. Weinberg-Witten theorem states that there isn't Poincare covariant stress-energy tensor for massless fields with helicity more than $1$. The only example of such higher helicity field is graviton. Thus stress-energy tensor which corresponds to theory of interaction of graviton with other fields isn't Poincare covariant one.

2. By the other side, we know that stress-energy tensor which is locally conserved one in General Relativity theory is just pseudotensor (it is called Landau pseudotensor) in a sense of General Relativity covariance. For its definition we need to choose local frame, which breaks general covariance of GR.

3. In flat space it can be shown that metric tensor (as well as 4-potential for gauge theories) isn't transformed as 4-tensor under Lorents transformations. Moreover, the requirement of Lorentz invariance of its theory coincides with the reqiurement of its gauge invariance.

By using these three statements I see some relation between necessity of Landau pseudotensor introduction, non-covariance of metric tensor and Weinberg-Witten theorem. WW theorem says that for graviton isn't possible to construct conserved Lorentz covariant stress-energy tensor. Thus tensor which is conserved have to be Lorentz non-invariant. This is true due to correspondence between gauge invariance of the gravity theory and its Lorentz invariance.

I.e., it seems that by using QFT we can make the prediction that it fundamental theory of gravity we can't introduce conception of localizable energy. It seems like prediction of equivalence principle of theory of gravity by using Weinberg's soft theorem.

Is this statement true?

• There are deep connections between qft and gr, and indeed one point of view is that you don't need to invoke geometry at all to discover gr, you are led to it simply by trying to construct a consistent field theory for an interacting spin 2 particle. See for example the feynman lectures on gravitation. – Andrew Jun 8 '15 at 1:08
• @Andrew : as for direct statement "gravity from gravitons", there are some doubts about its feasibility. Look here for the reference: arxiv.org/abs/gr-qc/0409089 . – Name YYY Jun 8 '15 at 14:51