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/Archive 1 — Preceding unsigned comment added by 81.131.80.137 ( talk) 19:57, 4 August 2012 (UTC)
Section "Lagrangian formalism" first has a subsection "Kinetic terms" with e.g.
Then, the next subsection is "Coupling terms" which contains e.g.
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)
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)
Neutrinos do not interact with photons. — Preceding unsigned comment added by 68.65.175.12 ( talk) 07:15, 3 September 2012 (UTC)
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)
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.
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)
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)
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. – LaundryPizza03 ( d c̄) 23:47, 29 April 2018 (UTC). – LaundryPizza03 ( d c̄) 23:47, 29 April 2018 (UTC)
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)
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)
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/Archive 1 — Preceding unsigned comment added by 81.131.80.137 ( talk) 19:57, 4 August 2012 (UTC)
Section "Lagrangian formalism" first has a subsection "Kinetic terms" with e.g.
Then, the next subsection is "Coupling terms" which contains e.g.
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)
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)
Neutrinos do not interact with photons. — Preceding unsigned comment added by 68.65.175.12 ( talk) 07:15, 3 September 2012 (UTC)
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)
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.
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)
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)
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. – LaundryPizza03 ( d c̄) 23:47, 29 April 2018 (UTC). – LaundryPizza03 ( d c̄) 23:47, 29 April 2018 (UTC)
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)
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)