Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A My T-shirt and the Standard Model

  1. Dec 11, 2017 #1
    This T-shirt I bought at a physics conference displays the following equation. It looks like the Lagrangian of the Standard Model of particle physics but I only recognise lines 1 (electroweak) and 3 (Higgs mechanism). What are lines 2 and 4 and what is/isn't included? eg. are quarks, gluons, Fadeev-Popov ghosts and Higgs ghosts all included? What about neutrino mass?
    ParticlePhysics_zpsvus9erah.jpg
     
  2. jcsd
  3. Dec 11, 2017 #2
    Line ##2## is a so-called kinetic term that describes the interaction of the different leptons and quarks amongst themselves. A kinetic term is a term with the derivative ##\partial## or the covariant derivative ##D##.

    Line ##4## is a so-called interaction term that describes the interaction of the leptons and quarks with the Higgs field. Interaction terms add richness to the theory. In this case, spontaneous symmetry breaking occurs within the interaction terms.

    Let me know if you'd like more details. I do not know your background, but I presume you are a newbie to the standard model of particle physics, so I have given a high-level overview without going into the details of what each term in lines ##2## and ##4## mean.

    P.S.: Gluon self-interaction is the third term in line ##1##. Neutrinos are massless in the standard model.
     
    Last edited: Dec 11, 2017
  4. Dec 11, 2017 #3

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    It is worth pointing out that the derivative needs to be covariant in order for the Lagrangian to be gauge invariant. The covariant derivative also contains a coupling to the gauge fields, which gives the minimal coupling of the fermions to the gauge fields.

    I would add that this particular type of interaction term are Yukawa couplings. It would also be more appropriate to say that the spontaneous symmetry breaking occurs in the gauge sector and does not necessarily have anything to do with the Yukawa couplings to fermions. However, upon SSB, the Yukawa couplings give rise to mass terms for the fermions.

    This is what the thread level indicator is for. In this case the A would mean that the reader has an understanding of the topic at graduate student level or higher. I believe the OP has used it incorrectly. (It is supposed to reflect the OP's level of knowledge, not the level of the topic itself.)

    It is worth pointing out that the gauge part contains both kinetic and self-interaction terms for all gauge fields.

    There are no ghosts included here. They appear once you look at gauge fixing and integrating out the redundant degrees of freedom that comes with gauge transformations.

    Indeed, as stated in #2, there are no neutrino masses in the standard model and consequently not in your Lagrangian.
     
  5. Dec 11, 2017 #4
    Thank you for the clarification. I was not fully qualified to reply to the post.
     
  6. Dec 14, 2017 #5
    Brilliant answers, both. Thank you.

    > I do not know your background, but I presume you are a newbie to the standard model of particle physics, so I have given a high-level overview without going into the details of what each term means.

    Yes, I'm a complete novice when it comes to the standard model, my expertise is Navier-Stokes and I'm self taught in quantum field theory.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...
Similar Threads for shirt Standard Model Date
A Conformal window Jan 22, 2018
I Standard Model (Forces interacting with Matter) Jan 8, 2018
A A symmetric model for leptons Jan 2, 2018
A Covariant derivative in Standard Model Nov 13, 2017
LHC t shirt formula Jun 10, 2010