Talk:Gluon field strength tensor

This is a terrible article and needs to be rewritten; unfortunately I do not have the knowledge nor the fortitude to do so. Thanks in advance for any future efforts. 147.188.248.179 (talk) 09:23, 4 February 2013 (UTC)

Potential inconsistencies/inaccuracies
There could be inconsistencies in signs multiplying gs and factors of 1/2... Need to check out what a "derivative acting on octet fields" actually means. M&and;Ŝc2ħεИτlk 07:46, 19 October 2013 (UTC)

Here is the section I'm on about, it's been removed since we don't seem to need it:

There is similar covariant derivative which acts on the color octet field:


 * $$\mathcal{D}_\mu =\partial_\mu \pm ig_s T^a \mathcal{A}^a_\mu\,,$$

where


 * $$(T^a)_{bc} = -i f_{abc}\,,$$

are 8 × 8 matrices, the adjoint representations of the SU(3) Lie algebra satisfying the commutation relations:


 * $$[T^a, T^b ] = i f_{abc} T^c\,.$$

just placed here for future reference. M&and;Ŝc2ħεИτlk 07:59, 19 October 2013 (UTC)

Transplant of curvature 2-form expression from Quantum chromodynamics to this article
See this cut and paste. Quantum chromodynamics gives the tensor expression for the Lagrangian and the gluon field strength:


 * $$G^a_{\mu \nu} = \partial_\mu \mathcal{A}^a_\nu - \partial_\nu \mathcal{A}^a_\mu + g f^{abc} \mathcal{A}^b_\mu \mathcal{A}^c_\nu \,,$$

which is enough for that article IMO. M&and;Ŝc2ħεИτlk 21:18, 20 October 2013 (UTC)

Gibberish
The IP said the article is terrible. Indeed, I am pretty familiar with such stuff as “tensor field”, “gauge group”, “vector bundle”, “differential form”, and “covariant derivative”, but hardly can understand anything here.

First of all, why is it called a tensor? To which bundle, or to the tensor product of which, does it belong? Before stating something about it, the entire section starting with “The tensor is denoted $G$, … and has components defined proportional” and ending “$G_{αβ}$ are actually 3 × 3 matrices, while $G^{a}_{αβ}$ are scalar components of a four dimensional second order tensor field” reads as a gibberish, especially scalar components. I can compute dimensions myself. What I need is some clue with a definition.

The Gluon field strength tensor section is also poor. If
 * $$\mathbf{G} =\mathrm{d}\boldsymbol{\mathcal{A}} \mp g\,\boldsymbol{\mathcal{A}}\wedge \boldsymbol{\mathcal{A}}$$

is a definition, then what is $g$? Where the article explains the nature of that symbol? What operation is assumed between the enigmatic $g$ and $$\boldsymbol{\mathcal{A}}$$? And how the section may contain a link to Élie Cartan, but miss a link to curvature form? Incnis Mrsi (talk) 20:17, 8 January 2014 (UTC)


 * I wrote what is in the sources provided.
 * The link to curvature form is easy to add. Sue me for missing the subscript "s" on the "enigmatic g" for the strong coupling constant. As you can see above from the (now corrected) section, I did not write the differential form equation, but it should be here. As far as I can make out the wedge product reproduces the term with the structure constants, but I don't know exactly, so left it. I haven't yet found a source for this particular expression.
 * The sources didn't give the relevant bundles. They just gave the definition in terms of the commutator of covariant derivatives.
 * My question - let's see you provide a source (or more) which gives a crystal clear and technically correct definition of the gluon field strength tensor as used in QCD? M&and;Ŝc2ħεИτlk 21:57, 8 January 2014 (UTC)


 * About "why is it a tensor?", because of the commutator of covariant derivative components, surely? Why is it (3 × 3)-matrix-valued? Because the covariant derivatives have contractions over the colour indices with the Gell-Mann matrices. There are 8 gluon colours, 8 GM matrices, and 8 gluon potentials, the covariant derivative contains a linear combination of all of them. M&and;Ŝc2ħεИτlk 22:08, 8 January 2014 (UTC)
 * There is a confusion about the word “scalar”. Your “scalar-valued components” is true in the sense “for certain coordinate system and fixed gauge we obtain scalar-valued functions”, but false in the sense “[for a fixed gauge] these functions transform under changes of coordinates as scalars”. It’s better to omit it to avoid ambiguities. Incnis Mrsi (talk) 08:04, 9 January 2014 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on Gluon field strength tensor. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Corrected formatting/usage for http://theory.fnal.gov/people/ellis/Talks/FNAL/l1_s.pdf

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.—cyberbot II  Talk to my owner :Online 02:50, 30 May 2016 (UTC)