LHC T-Shirt Formula: Unravel the Mystery

[rhenretta]

I went to see the LHC (my version of a pilgrimage to Mecca). I bought a tshirt with a formula on it, but I can't find any information on what the formula describes.


http://www.facebook.com/photo.php?pid=4005975&l=cc76e7a9d7&id=529304037

hopefully, that link works, if not I can tell you it is a formula describing L. I doubt in this case L is referring to angular momentum.

I am only on my iPhone, so unfortunately I can't transcribe the formula. I want to wear it, but I refuse until I understand the formula, lest I misrepresent myself.

 

[cristo]

I think it represents the electroweak part of the standard model lagrangian in a concise way: http://en.wikipedia.org/wiki/Electroweak_interaction

 

[Pinu7]

Please note that, in general, a fancy L in physics usually represents something called a "Lagrangian density."

 

[bapowell]

This is a Lagrangian density -- it contains all the dynamics of the theory (ie the equations of motion are derived from it). The first term:

$$-\frac{1}{4}F^{\mu \nu}F_{\mu \nu}$$

describes the gauge bosons (force carriers). In electromagnetism, the $$F^{\mu \nu}$$ is just the familiar field strength tensor (you can derive Maxwell's equations from this part of the Lagrangian!).

Second term:

$$i\bar{\psi}D\psi$$

describes the fermions in the theory. These fermions are interacting with the gauge fields (you don't see this directly here -- it's hidden in the $$D$$ term). So, in QED, these would be electrons, and the gauge fields they interact with are photons.

Third term:

$$\psi_i y_{ij}\psi_j \phi$$

is a Yukawa coupling between the fermions and a scalar field, $$\phi$$. This scalar is the elusive Higgs boson, and this term is responsible for giving the fermions masses. Very important ingredient!

Last terms:

$$|D_\mu\phi|^2 - V(\phi)$$

describes the Higgs boson. The first term is the kinetic energy (the field theory analog of half mv^2), and the second term is the potential energy of the field.

So, the shirt highlights some of the important ingredients of the standard model of particle physics.

EDIT: I shouldn't say this describes all the dynamics of the standard model -- the full SM Lagrangian is a monster. Rather, the t shirt displays some well known parts of it.

 

[Kevin_Axion]

This is the full Lagrangian Density for the Standard Model if you are interested in its impeccable length and complexity: http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html
And you're absolutely correct, it is Monster.
Also here's a Mathematical Formulation of the the Standard Model if you are interested; http://en.wikipedia.org/wiki/Standard_model_(mathematical_formulation))

 

[physstud]

Hey all,

I have a question concerning the Yukawa coupling terms... Shouldn't the first $$\psi$$ rather wear a bar such that the terms look like $$\bar{\psi}_i y_{ij}\psi_j\phi$$?? This keeps on confusing me (wearing the same T-Shirt and being asked from time to time... ;) )

thx in advance for some elucidation

 

[kurros]

Hey all,

I have a question concerning the Yukawa coupling terms... Shouldn't the first $$\psi$$ rather wear a bar such that the terms look like $$\bar{\psi}_i y_{ij}\psi_j\phi$$?? This keeps on confusing me (wearing the same T-Shirt and being asked from time to time... ;) )

thx in advance for some elucidation

I should think yes it should have a bar, otherwise the spinors don't contract properly. It is only schematic and lots of other things are suppressed so I wouldn't worry too much, except it is a bit inconsistent to put the bar and D-slash in the fermion kinetic energy/interaction term if you aren't going to bother with those details in the yukawa term.

 

[physstud]

that is exactly what I thought. OK, thanks for the confirmation ;-)

 

[3m0k177y]

I'm still confused about one thing. That is; what does the lagrangian describe?
When I look at this explanation, I just think that all this does is describe the higgs field. But, whenever I hear about this lagrangian, someone will say that it describes just about all of particle physics, but I don't see how it does that. Can someone please explain?
Thank you.

 

[bapowell]

There are many fields described by this Lagrangian, not just the Higgs. For example, the gauge boson Lagrangian, $f^{\mu \nu}F_{\mu \nu}$ would be there Higgs or no Higgs.

 

[kurros]

I'm still confused about one thing. That is; what does the lagrangian describe?
When I look at this explanation, I just think that all this does is describe the higgs field. But, whenever I hear about this lagrangian, someone will say that it describes just about all of particle physics, but I don't see how it does that. Can someone please explain?
Thank you.

From that Lagrangian you can compute the equations of motion for all the fields in the Standard Model. It is like a fancy version of F=ma.

 

[3m0k177y]

Oh, I get it all now. Thanks.

 

[3m0k177y]

Well, I get it all except for two things: the second and third terms. I din't quite understand them well, can someone go in depth on them please.
Thanks, once again.

 

[bapowell]

Well, I get it all except for two things: the second and third terms. I din't quite understand them well, can someone go in depth on them please.
Thanks, once again.

By 2nd and 3rd terms, do you mean the $\psi_i y_{ij} \psi_j \phi$ and the $|D_\mu \phi|^2$ terms?

 

[3m0k177y]

I mean the Yukawa coupling and the term that describes the fermions in the theory.

 

[Coin]

I got one of these shirts! There is an older thread with some people attempting to answer this same question.

My daydream is that someday the LHC will find a flaw or extension of the standard model, and then I can sew a patch onto the t-shirt correcting the lagrangian.

bapowell, thank you for your exhaustive post.