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LHC t shirt formula

  1. Jun 10, 2010 #1
    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 [Broken]

    hopefully, that link works, if not I can tell you it is a formula describing L. I doubt in this case L is refering 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.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 10, 2010 #2

    cristo

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  4. Jun 10, 2010 #3
    Please note that, in general, a fancy L in physics usually represents something called a "Lagrangian density."
     
  5. Jun 11, 2010 #4

    bapowell

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    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:

    [tex]-\frac{1}{4}F^{\mu \nu}F_{\mu \nu}[/tex]

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

    Second term:

    [tex]i\bar{\psi}D\psi[/tex]

    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 [tex]D[/tex] term). So, in QED, these would be electrons, and the gauge fields they interact with are photons.

    Third term:

    [tex]\psi_i y_{ij}\psi_j \phi[/tex]

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

    Last terms:

    [tex]|D_\mu\phi|^2 - V(\phi)[/tex]

    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.
     
    Last edited: Jun 11, 2010
  6. Jun 11, 2010 #5
    Last edited: Jun 11, 2010
  7. May 1, 2012 #6
    Hey all,

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

    thx in advance for some elucidation
     
  8. May 1, 2012 #7
    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.
     
  9. May 9, 2012 #8
    that is exactly what I thought. OK, thanks for the confirmation ;-)
     
  10. Jul 9, 2012 #9
    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.
     
  11. Jul 9, 2012 #10

    bapowell

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    There are many fields described by this Lagrangian, not just the Higgs. For example, the gauge boson Lagrangian, [itex]f^{\mu \nu}F_{\mu \nu}[/itex] would be there Higgs or no Higgs.
     
  12. Jul 9, 2012 #11
    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.
     
  13. Jul 9, 2012 #12
    Oh, I get it all now. Thanks.
     
  14. Jul 10, 2012 #13
    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.
     
  15. Jul 10, 2012 #14

    bapowell

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    By 2nd and 3rd terms, do you mean the [itex]\psi_i y_{ij} \psi_j \phi[/itex] and the [itex]|D_\mu \phi|^2[/itex] terms?
     
  16. Jul 10, 2012 #15
    I mean the Yukawa coupling and the term that describes the fermions in the theory.
     
  17. Jul 11, 2012 #16
    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.
     
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