By Sean Carroll | November 23, 2006 1:25 pm

Today we give thanks for the Lagrangian of the Standard Model of Particle Physics, after electroweak symmetry breaking, with no explicit Higgs boson.

SM Lagrangian w/o Higgs

It’s served us well for three decades, withstanding every challenge that particle accelerators could think to throw at it. But it’s going to be blown out of the water in a couple of years. Still, a pretty good run. Thanks, Standard Model Lagrangian!

  • mars

    Wow! Seems like a giant when you write it down like that!

  • Who

    No fooling Sean, natural law is great and wonderful and it is not amiss to sometimes be thankful for the lawfulness of the universe! I adapted this Thanksgiving hymn to round out the spirit of your post.

    O cosmic law, when I in awesome wonder,
    Consider all that evolution made,
    And witness stars, and hear the rolling thunder,
    Thy power throughout the universe displayed.

    Then sings my soul, o nature’s law, to thee,
    How great thou art, how great thou art.
    Then sings my soul, o nature’s law, to thee,
    How great thou art, how great thou art!

    [pardon the poetic license taken of addressing the laws of physics despite their not being a person]

  • Maynard Handley

    Surely this is not correct, Sean? You only have one generation, and, apart from simply saying “repeat three times” there have to be coupling terms.

    More to the point, is this really the simplest version, and is it useful (apart from scaring children and writing computer programs) to display a form more complicated than the ideal?

    If we switch to appropriate linear combinations of A/W/Z and write the dirac terms in something that is more obviously a gauge term like
    e(d- A~ -m)e (where A~ is the appropriate linear combination), can’t we get this to something quite a bit cleaner?
    The L/R weak stuff is always going to be messy, but my understanding was that everything else could be gathered up quite neatly.

  • Sean

    Maynard, this is in the mass-eigenstate basis, where the CKM matrix comes into the couplings to the weak bosons, and there’s no explicit mixing in the mass terms.

    On the other hand, I make no claims that it’s correct! It’s just a file I dug up from when I was teaching the course, and I tried to remove the Higgs terms by hand. I already noticed that I had removed the W/Z mass terms by accident, so they’re now back in.

    Of course it could be much simpler. As Feynman long ago pointed out, any equation can be written U=0, for some appropriate definition of U. Some forms are good for different reasons. An explicit form like this is good for figuring out propagators and Feynman rules.

  • Count Iblis

    Since we are described by the Standard Model, the Standard Model is thanking itself :)

  • Chris W.

    Indeed, Count Iblis, and perhaps someday some important questions about the Standard Model will be answered by thinking more deeply about what that remark might actually imply.

  • Vince

    No, no, Count,

    We are described by the theory of everything coupled to the mental faculties not described by physics, like our ability to reason…

    and free will.

  • Vince

    Actually, we are described by physics coupled to aspects of the mind not explanable by mechanistic materialism.

  • Aaron


    As if I needed another reason not to go into particle physics! I do, however, think that the steady stream of “here…” “where…” “and…” “and…” “where…” is very classy. :)

  • Alejandro Rivero

    And no explicit ghosts, neither.

  • WeemaWhopper

    Any QCD in there?

  • Douglas

    As an undergraduate, I have to say that this post was especially exciting for all the physics it promises I’ll learn in graduate school. Oh my god, oh my god!

  • Sean

    Someday, Douglas, you’ll be finding typos in equations like this one. But you’re right, the physics behind it is truly amazing!

  • man

    Man, you need a life…and by that I really mean…Man, you need a wife…

  • Count Iblis

    Any QCD in there?

    The first term of L_{gauge} and the first term of L_{gauge/psi} :)

  • Count Iblis

    Vince, free will is just an illusion. Without any external influence, what you will do in the future depends only on what is exactly going on in your brain. But you can’t be aware of everything that is going in your brain because the brain stores a lot of other information besides keeping an eye on itself.

  • Vince

    Thank you, Count, for destroying the idea of loving another person. Whether or not a marriage works out depends on physical state of the brain and the world. What all the particles are doing at that time, that is. Hear that, y’all?

  • Vince

    Hey, at least the statement “fate brought us together” now means something.

    Okay, better go now and execute some more of my internal source code.

  • Count Iblis

    Vince, clearly we can love another person, so that idea cannot be destroyed by anything. You should turn this problem around and conclude that given the fact that we can love other person, the laws of physics allow for that.

  • Vince

    Does love follow from the standard model? What is your definition of love anyway? If everything about us is governed by and a product of the laws of physics, then the only thing love can be is a feeling. We don’t decide who we choose to love not only because there is no such thing as free choice but also because love is reduced to feelings which are a manifestation of brain chemistry governed by the laws of physics, and we do not will the feelings we have for people.

  • fqassemi

    Hi to all, owners and contributors.
    After a long reading of this blog I joined to add something, although I would like to share my ideas on lots of discussions but I would like to add about this topic which I, presently, I engage with. My point is on the name of this huge Lagrangian. I think the name is better understood if one says “Standard model of particle Physics INTERACTION”. The fight is not on the name but is on what we expect from this functional. Quantum Mechanics came in to explorer shortages of classical physics but later on with Heisenberg suggestion just observables(!) were considered ( as a matter of fact I think it is rather pragmatic view point). I don’t extract this issue more and say my point, finally our QFT were invented to explain INTERACTION between elementary particles nothing more about origins! So, the problem becomes ambiguous when for example GR come into account where based on Einstein theory it is not about interaction!


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Cosmic Variance

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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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