Generalized free fields as dark matter?

  • #1
Peter Morgan
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@vanhees71 reminds us that
The only interpretation of particles is in terms of asymptotic free states, and the observable predictions are in S-matrix elements.
which suggests something I've wondered about for a while, whether dark matter might be adequately modeled by generalized free fields, which do not have asymptotic free states. Ray Streater, in Rep. Prog. Phys. 1975 38 771-846, "Outline of axiomatic relativistic quantum field theory" has this account:

upload_2018-4-6_7-43-55.png

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[I'd be pleased to know of a clear, more recent reference.]
The really pertinent phrase is "If the Källén-Lehmann weight function is continuous, there are no particles
associated with the corresponding generalized free field". Such a free field clearly exhibits different translation/mass properties than a free field that has a singular mass distribution, and yet as far as local properties of such a generalized free field are concerned, we can introduce a mass distribution that is as close to singular as we like, so that the local behavior, out to many light years, say, would be identical. Of course although we only compute the S-matrix between states at asymptotic separation, we in fact only measure the distribution of events in detectors in high energy experiments at separations up to a few meters (up to hundreds of kilometers for the outliers, neutrinos).
What studies are there of such a suggestion in the dark matter literature?
Is my understanding that unparticles have been suggested (but not successfully) as a model for dark energy correct?
 

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A. Neumaier
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Why should generalized free fields describe dark matter? Speculating in the dark about the dark leads nowhere.
 
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Peter Morgan
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Why should generalized free fields describe dark matter? Speculating in the dark about the dark leads nowhere.
I believed I was asking whether anyone has considered whether this speculation might make contact with experiment at least far enough for it to be published. I'm also happy enough to think about the consequences of generalized free fields (and whatever deformations might be introduced thereof) purely as mathematics, which might or might not lead to some connection with local experimental data.
Thanks for your "Introduction to coherent spaces" paper and its pursuants, BTW. Nice math: I like the finite control it emphasizes instead of axiomatically insisting on infinite-dimensional representations of the Poincaré group as a starting point (of course I do: you'll find the same concern, but more implicitly, in the emphasis on manifest invariance under the Poincaré group instead of on representation in my arXiv:1709.06711).
 
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A. Neumaier
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consequences of generalized free fields (and whatever deformations might be introduced thereof) purely as mathematics
Generalized free fields have no Lagrangian formulation. Hence it is completely unclear how to couple them to the standard model or to general relativity. But coupled to nothing they cannot affect anything, hence cannot be dark matter.
 
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Peter Morgan
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Generalized free fields have no Lagrangian formulation. Hence it is completely unclear how to couple them to the standard model or to general relativity. But coupled to nothing they cannot affect anything, hence cannot be dark matter.
Right. I'm more engaged in constructing deformations of free field Wightman functions, possibly including generalized free fields, what Haag (page 61 of LQP, 2nd Ed.) more-or-less calls a "nonlinear program", for which, speaking loosely, I take Lagrangian methods to produce an asymptotic expansion. In a nonlinear program, coupling, not being presented as an asymptotic expansion, does not take the same form as in a Lagrangian approach. I'm trying to move in different circles, as it were. Whether I will produce anything interesting to anyone else before I die is a question, of course, but semper memento vivere.
 

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