What is the purpose of Faddeev-Popov ghosts in the standard model lagrangian?

In summary: 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).Yes, there are different ways to break the Lagrangian into pieces. The most common is probably to break it into its gauge (here U(1), SU(2) and SU(3)) pieces, which are computed separately and combined to form the complete Lagrangian.The most convenient place to do this is in the path integral for the theory, because the path integral allows you to integrate over configurations that are related by gauge transformations. My guess is that most people who study this stuff (at least in a formal setting)
  • #1
um0123
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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 I am 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.
 
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  • #3
  • #4
um0123 said:
http://nuclear.ucdavis.edu/~tgutierr/files/sml2.pdf

that can't be a REAL exercise question. can it!?
The website 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. :biggrin:
um0123 said:
btw, thanks for the response, but is there a way to get that pdf into an image?
Now this is not really a physics question anymore o:)
I attached the pdf converted to png, hopefully that suits your puproses
 

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  • #5
humanino said:
The website 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. :biggrin:
Now this is not really a physics question anymore o:)
I attached the pdf converted to png, hopefully that suits your puproses

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
oh i forgot to ask, why is when i type standard model lagrangian on google it comes up with a different equation. One that isn't a completely connected equation. Like this:

sm-lagrangian1.gif


Is that related to it? it must be, google wouldn't lie to me.
 
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  • #7
#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
hamster143 said:
G, X, and Y
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
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 [tex]\phi[/tex]'s are also ghosts? That's a very ghostly lagrangian ...
 
  • #10
hamster143 said:
G is not the glue field
You are right, my bad, I should have paid attention, there is no graviton. Thank you for the correction.
hamster143 said:
That's a very ghostly lagrangian ...
Indeed, all bosons have their ghosts.
Y for the photon, 3 X's for the weak vectors, 8 G's for the gluons, and [itex]\phi[/itex]'s for the charged and neutral Higgs' ghosts.
 
  • #11
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
um0123 said:
ghosts? scary! Do i need to have advanced mathematical knowldege to know what those are? or can it be explained to me?
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.
http://en.wikipedia.org/wiki/Faddeev-Popov_ghost
 

Related to What is the purpose of Faddeev-Popov ghosts in the standard model lagrangian?

1. What is the Standard Model Lagrangian?

The Standard Model Lagrangian is a mathematical equation that describes the fundamental particles and forces in the universe, as well as their interactions. It is the cornerstone of the Standard Model of particle physics, which is the most successful theory we have for understanding the fundamental building blocks of our universe.

2. What does the Standard Model Lagrangian include?

The Standard Model Lagrangian includes all the known particles in the universe, including quarks, leptons, and force-carrying particles like photons and gluons. It also includes the forces of nature, such as the strong, weak, and electromagnetic forces.

3. How was the Standard Model Lagrangian developed?

The Standard Model Lagrangian was developed through a collaborative effort by many scientists over several decades. It was first proposed in the 1960s and has been refined and improved upon over the years with the help of experimental data and theoretical advancements.

4. What are the limitations of the Standard Model Lagrangian?

While the Standard Model Lagrangian can accurately describe the behavior of particles and forces at the energy scales we have access to, it has limitations. It does not account for gravity, dark matter, or dark energy, and it cannot explain certain phenomena like the hierarchy problem and the matter-antimatter asymmetry in the universe.

5. What are the implications of the Standard Model Lagrangian for our understanding of the universe?

The Standard Model Lagrangian has been incredibly successful in predicting and explaining the behavior of particles and forces in the universe. It has allowed us to make precise calculations and predictions, and has been confirmed by countless experiments. However, it also highlights the gaps in our understanding and the need for further research to fully understand the complexities of the universe.

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