Talk:Mathematical formulation of the Standard Model

/Archive 1 — Preceding unsigned comment added by 81.131.80.137 (talk) 19:57, 4 August 2012 (UTC)

Remove kinetic terms from coupling terms?
Section "Lagrangian formalism" first has a subsection "Kinetic terms" with e.g.
 * $$i\bar{\psi}\gamma^{\mu}\partial_{\mu}\psi$$.

Then, the next subsection is "Coupling terms" which contains e.g.
 * $$ \mathcal{L}_\mathrm{EW} = \sum_\psi\bar\psi\gamma^\mu \left(i\partial_\mu-g^\prime{1\over2}Y_\mathrm{W}B_\mu-g{1\over2}\boldsymbol{\tau}\mathbf{W}_\mu\right)\psi$$

Well... the second formula contains the first as the first term, when you expand the brackets. This is not what the article implies: that fermion's terms are kinetic_terms + coupling_terms.

I propose removing kinetic term from coupling terms. — Preceding unsigned comment added by 185.5.69.233 (talk) 22:35, 22 June 2023 (UTC)

Rewritten article
Thanks mostly to the contributions from this user, I've completely rewritten this article. Hopefully it is now somewhat cohesive and comprehensive, and will be helpful to some people. There are probably a few mistakes, especially with formatting, as I haven't edited much before.

I'd say the thing it lacks most is a good discussion of interaction terms, and probably also a few citations.

Cheers, Euan 81.131.80.137 (talk) 20:02, 4 August 2012 (UTC)

Interaction Graph
Neutrinos do not interact with photons. — Preceding unsigned comment added by 68.65.175.12 (talk) 07:15, 3 September 2012 (UTC)

The diagram is now wrong for a different reason
The blue arc between electrons and neutrinos indicates an interaction that does not exist. The relationship is one of grouping, not interaction. Someone should fix this. I recommend placing an oval around all the leptons, linking W and Z to the oval (indicating all leptons), and an arc from photons, crossing that oval, to the charged leptons. 129.67.118.100 (talk) 16:07, 14 April 2014 (UTC)

There is a newer and better interaction graph (created 2014) in the main Standard Model article. I suggest using that same interaction graph in this Standard Model (mathematical formulation) article. K.enevoldsen (talk) 03:26, 17 August 2015 (UTC)

The Standard Model Chart also needs repair
First, there are 8 g's, not just 1: g₁, ..., g₈. Second, the T₃ gauge charge assignments for the W's: (W⁺, W³, W⁻): (+1, 0, -1) are the T₃ eigenstates, with (W¹,W²) being superpositions of the T₃ eigenstates (W⁺,W⁻). Third, quark and anti-quark colors comprise 6 cardinal points in the (λ₃,λ₈)/2 plane (where λ₁, ..., λ₈ are the Gell-Mann matrices) that form a hexagon centered about (0,0), with (red,green,blue) = ((+1/2, +1/√12), (0, -1/√3), (-1/2, +1/√12)), and anti-(red,green,blue) = ((-1/2, -1/√12), (0, +1/√3), (+1/2, -1/√12)) corresponding to the positions that would be occupied by (cyan,magenta,amber) in the Newton color wheel. The (λ₃,λ₈)/2 charges play roles, here, analogous to the chromaticity coordinates in color theory: (λ₃,λ₈)/2 corresponds roughly to the (x,y) chromaticity coordinates in CIE1931, except for the quark and anti-quark eigenstates being centered about 0. Fourth, the SU(3) gluon eigenstates form a flattened cube in the (λ₃,λ₈)/2 plane, with (g₃,g₈) at (0,0); and (g₁,g₂), (g₄,g₅), (g₆,g₇) each pairing off to produce SU(3) eigenstates, in the same way that (W¹, W²) pair off to produce (W⁺, W⁻). The 6 gluon eigenstates lie at angles (30, 90, 150, 210, 270, 330) degrees in the (λ₃,λ₈)/2 plane, where (red,green,blue) are set at (0,120,240) degrees, and lie at a distance √3 further out from the origin; i.e. the 6 colored gluon SU(3) eigenstates have √3 times the charge of the quark eigenstates at angles half way between the those of the 6 cardinal points formed by the quark/anti-quark charges. The eigenstates formed from (g₁,g₂) are on the (30, 210) degree axis, while those formed from (g₄,g₅), (g₆,g₇) reside respectively on the (90, 270) and (150, 330) degree axes.

Lagrangian
The description of the Lagrangian is not in line with the linked description from einstein-schrodinger.com. Why not ? Forcefield2 (talk) 18:20, 6 October 2013 (UTC)

Weyl fermions
Within the last several days, a group headed by Princeton has reported observation of Weyl fermions. Is this a topic that should be mentioned in this article? Articles I've read in media suggest it is a massless fermion that carries electrical charge. --74.38.77.101 (talk) 21:07, 21 July 2015 (UTC)


 * That's an interesting find, but to my (admittedly limited) knowledge, that find would probably be more suited to an article about Weyl fermions themselves, or maybe something like quasiparticles or solid-state physics, as I believe the observation was not that of a "fundamental" Weyl fermion, but rather or a quasiparticle within condensed matter, which is qualitatively somewhat different. I could be wrong, but I don't believe it's a game changer for the Standard Model itself.  — Preceding unsigned comment added by 70.247.166.192 (talk) 00:31, 2 September 2015 (UTC)

Requested move 29 April 2018

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section. 

The result of the move request was: moved as requested per the discussion below. Dekimasu よ! 20:01, 6 May 2018 (UTC)

Standard Model (mathematical formulation) → Mathematical formulation of the Standard Model – A more natural title than current. Also see Mathematical formulation of quantum mechanics. – Laundry Pizza 03  ( d c&#x0304; ) 23:47, 29 April 2018 (UTC). – Laundry Pizza 03  ( d c&#x0304; ) 23:47, 29 April 2018 (UTC)
 * Good idea. The disambiguation-style title is not appropriate here: 'Standard Model' in both titles referes to the same thing. — dukwon (talk) (contribs) 10:29, 30 April 2018 (UTC)


 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Weak charge
I was reading some things about weak charge. That article was just a redirect to this one, which didn't have any explanation, so I stubbed something for it based on a few papers. I know what the magnitude of the weak charge is, more or less, and that you can tot it up in a nucleus, but it would sure be nice to get expert explanation of what it is, and its relationship if any to weak isospin and weak hypercharge and Weinberg angle and so on. Wnt (talk) 03:37, 13 November 2018 (UTC)


 * I would strongly resist association of the weak charge stub to this article. This is an eccentric/parochial usage used only in nuclear and atomic physics, and not in particle physics, defined in, e.g. .  It is but the vector coupling of the Z-boson to the nucleon, gV, whose currents are exemplified in the last formula of this article, and in W and Z bosons.  While the linked definition and reference could usefully be adduced in that stub, any mention of such here would only serve to muddy waters and confuse the reader. Cuzkatzimhut (talk) 20:45, 13 November 2018 (UTC)

The full equation for the standard model


What I would like to see here is the full equation for the standard model, with every variable and operator explained. Something like what's presented here or at 43:16 here. I think its totally fine to have complex terms or functions or operators as long as we link to somewhere where each can be worked out. Its much better to have a short equation like this where you can see the structure, rather than something like this that has inlined way too much of the functions to be able to see anything at a glance. Can anyone comment on the equations given in my first two links as to whether they're accurate, and whether the variables are understandable enough to be able to list out what they are? Fresheneesz (talk) 04:16, 16 January 2019 (UTC)


 * The equations are correct, but deeply uninformative, except as summaries of a logically troubled background--you should have spotted the nasty failure to include the Yukawa couplings into the Higgs sector: this is the second job of the Higgs, for crying out loud. The Symmetry Magazine exemplar is classic "Lies to Children" chartjunk, all formally correct of course, but profoundly corrosive to understanding: it is  not in the unitary gauge!, and as a result it displays unphysical Goldstone degrees of freedom; downright misleading and hostile to the novice. Still, I added a link to the SM Lagrangian in WP you apparently missed in a more prominent location.
 * WP is not a tutorial on the standard model. There are books, summaries, and, of course, Wikiversity for that. I strongly believe insertions of this type would damage the article, depredated upon massively, already. Cuzkatzimhut (talk) 17:05, 16 January 2019 (UTC)