# Heisenberg's Unified Field Theory

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In PSE I have asked this question. My confusion was due to the contradiction between the languages of this paper and . What had been the reasons behind the revival of Heisenberg's Unified Field Theory? Isn't String Theory a 'good and effective' candidate for the Theory of Everything?

asked Oct 7, 2014
edited Oct 7, 2014

Hi user170039, welcome to PhysicsOverflow.

Maybe it would help your question getting more positive attention, if you could summarize in a short parapraph what Heisenberg's Unified Field Theory is? The talks you linked too look interesting, but it takes me at least some time to read and understand them.

## 1 Answer

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Heisenberg's unified field theory was a 1950s attempt to build everything out of one field. The distinction with Einstein's program is that Heisenberg takes the field to be fermionic. The fermions don't have to be constructed, rather the bosons, but bosons are fermion pairs.

So the natural idea was to reproduce all the scalars using Fermionic bilinears with a vacuum expectation value. Scalars would come from fluctuations in scalar expectation values, tensors from tensor expectation values, and so on. The idea failed as you can't make a real graviton, with its gauge invariance and ward identity, as a local bound state of Fermions, or anything else, any attempt to do this is nowadays generally brushed aside by saying "Weinberg-Witten theorem".

The way to make an emergent graviton is holographically, using a nonlocal boundary-bulk mapping, and this is string theory. The graviton emerges, but not as a local bound state of other fields.

Still, a part of Heisenberg's idea survives today inside a correct theory, in the quark condensate of QCD. This is a Heisenberg style fermion bilinear condensate, and the pions and kaons are the lowest-energy sloshing of this condensate. You can also understand the rho, the omega as effective excitations of this condensate, and the nucleon as a topological defect. Nambu was aware of Heisenberg's ideas, if I remember correctly, but unlike Heisenberg, he made a much more limited claim, and also, a correct claim.

The modern TOE versions reviving Heisenbergs idea are not viable because if they are doing gravity, they conflict with Weinberg-Witten. There is also no point in this exercise anymore, as we know the field content of nature, and having one uber-fermion is no more compelling than having the standard model.

answered Oct 8, 2014 by (7,720 points)

@RonMaimon: But, so far as I know the existence of Gravitons is yet to be confirmed. What if Gravitons don't exist?

@user170039: Here is a paper on the Weinberg-Witten theorem and its context.

@user170039 there are plenty of good theoretical reasons why the gravitational field can be assumed to be quantized too (in the same way as all other fields corresponding to the fundamental forces are quantized), and the corresponding quanta are called  gravitons.

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