Talk:Landau pole

Though these concepts are new to me (I'm still working on finishing my physics BS), there are a couple of spots in this article sporting some "loose" language. For instance, the sentance "Nevertheless, the Landau pole is an awkward theoretical feature of QED, a sufficiently awkward one to make us look for a better theory." near the end of the article is ambiguous. Who is "we"? How are "we" looking for a new theory? What makes the Landau pole so awkward? QED is generally well accepted and these kinds of suggestions should be made much more clearly, and with reference to other articles/materials on the subject, I believe.

Also, I feel that allusions to superstring theory should be made very carefully in all physics articles that are not directly related to superstring theory, as it is still not considered to be a true theory by a majority of the scientific community.

-Andrew Hagler (hags2k@gmail.com)

Can anyone find the actual value of the renormalised charge eR expressed in the unitless way it appears to be in QED? I'm guessing units where h=c=1; is that enough to make charge dimensionless? Anyway it would be interested to see the actual &Lambda; scale numerically.


 * When $$\hbar=c=1$$, the (usual) electron charge is $$e=\sqrt{\alpha}=\sqrt{1/137.\ldots}$$. I cannot find $$e_R$$, as I'm not sure I understand the formula right. 193.125.71.14 (talk) 14:09, 21 August 2009 (UTC)

This article definitely needs some attention, but I don't have time now to do it properly, so I'll make just a brief comment: You can find some of the answers to the previous question under fine-structure constant. The correct version of the previous expression, in the usual units $$\hbar = c = \epsilon_0 = 1$$ is $$e_R^2 = 4\pi\alpha_R$$, where I have included subscripts R to make it clear that both sides are renormalized. The value of $$\alpha_R$$ = 1/137... is the Thomson limit, at zero momentum transfer. In SI units, this value corresponds to $$e_R \approx 1.6\times 10^{-19} C$$. The bare parameter e appearing in the Lagrangian is infinite (not just "somewhat different" from eR). $$\Lambda$$ does not have a universal "value" because it depends on the measurement. The article should avoid questionable or unproven statements, such as the one that string theory is free of Landau poles. The article could use some expansion, and a cleaning-up to either remove or substantiate the "citation-needed" items. Dusty14 (talk) 15:35, 14 May 2010 (UTC)

Update, May 2010
I think this deserves more attention and expansion, but I made a start. The main changes were to add some in-line references, and to reverse the misleading statement suggesting that the Landau pole is a perturbative relic. It is clearly seen in lattice calculations, including three that are now cited. One of these refers to a possible resolution of the pole problem, but this appears to apply only to a particular lattice model, not real QED, so I believe it is beyond the scope of this article. (Anyone who could possibly understand this would be able to read the articles provided.) The unnecessary speculation on string theory is removed, both because it is irrelevant to the topic, and because I am not aware of any proof that string theory is free of Landau poles. (Speculations don't belong here.) I also put in a numerical value, which addresses the above question in the talk page, and tried to remove unnecessarily technical language. I added a new section "Beyond QED" which points out that the existence of a pole at the landau scale is practically irrelevant, since QED is not a complete theory on its own. This section also mentions the Higgs case, which perhaps should be expanded. The Landau pole also appears in applications of field theory outside of particle physics. A section on this should be added as well. Dusty14 (talk) 17:24, 14 May 2010 (UTC)

Question
I feel like the very first sentence in this article is wrong - "In physics, the Landau pole or the Moscow zero is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite." By this definition, QCD has a landau pole at $$ \Lambda_{QCD} $$ but this seems incorrect. Shouldn't it be more like 'A Landau pole is an energy scale at which the coupling constant becomes infinite in the UV' ? — Preceding unsigned comment added by 128.84.4.251 (talk) 15:16, 14 June 2012 (UTC)

Ambiguous sentence in introduction
In the third paragraph of the introduction section the second last sentence is "Numerical computations performed in this framework seems to confirm Landau's conclusion". From the preceding sentences I cannot discern what "Landau's conclusion" actually is and so this sentence conveys no information to me. (Bjfar (talk) 02:23, 24 January 2013 (UTC))


 * I was also confused by that sentence. I looked up the papers it was refering to and hopefully changed it to something that's more clear 94.226.42.172 (talk) 11:12, 28 November 2021 (UTC)