Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Triviality Pursuit: Can elementary scalar particles exist?

Originality
+ 1 - 1
Accuracy
+ 2 - 1
Score
1.00
2477 views
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 5, 1988 to Reviews I by  (no author on PO assigned yet) 
  • [ revision history ]
    retagged Jul 29, 2015
    Most voted comments show all 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?

    @ 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 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".

    @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.

    Your Review:

    Please use reviews only to (at least partly) review submissions. To comment, discuss, or ask for clarification, leave a comment instead.
    To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
    Please consult the FAQ for as to how to format your post.
    This is the review box; if you want to write a comment instead, please use the 'add comment' button.
    Live preview (may slow down editor)   Preview
    Your name to display (optional):
    Privacy: Your email address will only be used for sending these notifications.
    Anti-spam verification:
    If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
    p$\hbar$ysicsOver$\varnothing$low
    Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
    Please complete the anti-spam verification




    user contributions licensed under cc by-sa 3.0 with attribution required

    Your rights
    ...