Standard model lagrangian?

1. Jul 14, 2009

um0123

Does anyone have a high resolution picture of the standard model lagrangian? i want to put it on a t shirt and give it to my math teacher who worked at Bell Laboratories for 10 years and knows just about everything about physics and math.

P.S. i only think its called the standard model lagrangian, what im talking about is the really long equation that takes up like a long scroll.

P.P.S. A picture of the equation itself and not the scroll with the original equation is just as good.

2. Jul 14, 2009

humanino

3. Jul 15, 2009

um0123

4. Jul 15, 2009

humanino

The web site author calls it "fun yet soul-crushing exam question". Whether it may be real depends on the cruelty of the teacher convoluted with the talent of the students.
Now this is not really a physics question anymore
I attached the pdf converted to png, hopefully that suits your puproses

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• sm.jpg
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5. Jul 15, 2009

um0123

Haha, what teacher would do such a thing!!!

and thanks for the image conversion, i know it wasnt a physics question or even anyones responsability but my own, so i think you for the effort.

6. Jul 15, 2009

um0123

oh i forgot to ask, why is when i type standard model lagrangian on google it comes up with a different equation. One that isnt a completely connected equation. Like this:

Is that related to it? it must be, google wouldnt lie to me.

Last edited by a moderator: Apr 18, 2017
7. Jul 15, 2009

hamster143

#1 only contains matter-related terms in compact notation, it's missing all Higgs-related terms (all terms with H from the original link) and all gauge field self-coupling and propagation terms.

#2 only contains electroweak terms (GWS subscript stands for Glashow-Weinberg-Salam).

Humanino's link, on the other hand, contains, in addition to usual SM, some stuff which I'm having trouble identifying right away (what's G, X, and Y, for example?)

8. Jul 15, 2009

humanino

X and Y are ghosts, and IIRC G is the glue field (g is the graviton, so depending with whom the f's are, they represent different structure constants).

9. Jul 15, 2009

hamster143

I can accept X and Y to be ghosts, though they shouldn't really be part of the lagrangian. G is not the glue field, two-index g is: notice that the fourth term couples gluon with two quarks. G couples to itself (fifth term) and there's a vertex between two G's and a gluon (sixth term), and it has no other interactions.

I'm guessing that $$\phi$$'s are also ghosts? That's a very ghostly lagrangian ...

10. Jul 15, 2009

humanino

You are right, my bad, I should have paid attention, there is no graviton. Thank you for the correction.
Indeed, all bosons have their ghosts.
Y for the photon, 3 X's for the weak vectors, 8 G's for the gluons, and $\phi$'s for the charged and neutral Higgs' ghosts.

11. Jul 15, 2009

um0123

ghosts? scary! Do i need to have advanced mathematical knowldege to know what those are? or can it be explained to me?

So there are different types of the standard model lagrangian to calculate different things, and the one that humanio posted is the one that includes everything (even the higgs which hasnt been discovered).

Do each have names, like is the first one i posted call the Matter Lagrangian? and would the second be the Electro-weak Standard model?

12. Jul 15, 2009

humanino

They are not as romantic as their Faddeev-Popov name suggests. Mostly they enable us to conveniently include a jacobian in a path integral, where the jacobian is necessary because we have a delta function to enforce gauge invariance.