Triviality Pursuit: Can elementary scalar particles exist?

Question

Referee this paper: Phys.Rept. 167 (1988) 241 RU-87-B1-20 by David J.E. Callaway

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

(Is this your paper?)

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Great effort is presently being expended in the search for elementary scalar ``Higgs'' particles. These particles have yet to be observed. The primary justification for this search is the theoretically elegant Higgs-Kibble mechanism, in which the interactions of elemetary scalars are used to generate gauge boson masses in a quantum field theory. However, strong evidence suggests that at least a pure phi ⁴ scalar field theory is trivial or noninteracting. Should this triviality persist in more complicated systems such as the standard model of the weak interaction, the motivation for looking for Higgs particles would be seriously undermined. Alternatively, the presence of gauge and fermion fields can rescue a pure scalar theory from triviality. Phenomenological constraints (such as a bounded or even predictable Higgs mass) may then be implied. In this report the evidence for triviality in various field theories is reviewed, and the implications for high energy physics are discussed.

Comments

@dimension10, even by today's knowledge $\phi^4$ is quite possibly trivial, it's more about the mathematical structure than phenomenology.

I haven't read the paper, but it's a bit strange for the abstract to say 

Should this triviality persist in more complicated systems such as the standard model of the weak interaction, the motivation for looking for Higgs particles would be seriously undermined.

Wouldn't the same comment apply to QED? By 1988 people should already know QED is quite possibly trivial, nonetheless describes reality very well, @RonMaimon could you comment on this?

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@ VladimirKalitvianski: Not every interaction means decay. It can just be scattering, as for a repulsive potential in the nonrelativistic case. 

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I have finally skimmed through the review. This is a pretty comprehensive(possibly all-encompassing) review of renormalization and triviality/Landau pole problem, from abstract theories to their phenomenologies. I don't think I understand all the content, but the parts I do understand(which is a non-negligible portion) are fairly accurate, +1 to accuracy.

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@JiaYiyang Do not hurry to vote for accuracy if there is still a part you do not understand. If you are excited, then write "So far I am excited with this review".

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@JiaYiyang: Wouldn't the same comment apply to QED? By 1988 people should already know QED is quite possibly trivial, nonetheless describes reality very well

Unlike the standard model, QED has no scalar particle. Therefore the triviality issues, though nontrivial for QED, too, are different than those for $\Phi^4_4$ or the standard model.

By the way, I believe that neither $\Phi^4$ theory nor QED are trivial; the techniques that suggest it are based on particular constructive approaches that are likely to fail. But there are alternative constructive principles where the verdict is still out. E.g., Klauder's affine approach has not been investigated from the rigorous point of view and might well lead to a construction.

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@JiaYiyang:  In the absence of information, only refraining form betting is rational.

IF QED exists at low energies the Wightman axioms imply that it exists at all energies. If you are interested in other positive theoretical evidence for the nontriviality of QED, ask a corresponding question!

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@ArnoldNeumaier, done, it's here.