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  Triviality Pursuit: Can elementary scalar particles exist?

+ 1 - 1
+ 2 - 1
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?)

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.

summarized by Dilaton , dimension10
paper authored Mar 6, 1988 to Reviews I by  (no author on PO assigned yet) 
  • [ revision history ]
    retagged Jul 29, 2015
    Most voted comments show all comments

    This is a review, so originality is not a concern.

    @Dimension10 I think older papers that correctly made use of the state of the art knowledge valid at the time they have been written and have therefore been correct at the time of publishing, should not be downvoted because our knowledge has now changed/deepend/improved, etc ...

    Otherwise, all phenomenological papers writing about BSM models that are excluded by now, would get downvoted too for example ...

    This would be not a good idea, one can not expect authors to know and include the future state of the art into their work or to know in advance what will be known in the future etc....

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

    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.

    @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.

    Most recent comments show all comments

    @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!

    @ArnoldNeumaier, done, it's here.

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