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

Basic question about Feynman Diagrams

  1. Feb 9, 2012 #1
    Can a vertex of a Feynman diagram have more than three particles going in or out from it? Assuming all other conservation laws are obeyed, of course. I haven't seen this being explicitly stated but all the Feynman vertices I have seen have three arms attached. Thank you.
  2. jcsd
  3. Feb 9, 2012 #2
    You can indeed. For instance gluons can make a 4 vertex.
  4. Feb 9, 2012 #3


    User Avatar
    Science Advisor

    An interaction term in the Lagrangian which is trilinear leads to a 3-particle vertex, while one which is quadrilinear leads to a 4-particle vertex. These things occur for example in electroweak theory. The kinetic energy term for the W boson is 1/4 WμνWμν where Wμν = ∂μWν - ∂νWμ - gWμ x Wν, which leads among other things to a 4-particle WWWW vertex. Also there is a WWhh vertex from its interaction with the Higgs.
  5. Feb 9, 2012 #4
    Thank you for the quick replies. I do not know about the interaction terms in the Lagrangian. I am just learning to draw Feynman Diagrams for basic QED and Weak Force processes. So, in these cases, are my vertices 3 vertices or 4 vertices or are both okay? Thank you.
  6. Feb 9, 2012 #5


    User Avatar
    Science Advisor

    In QED, the interaction term from the Lagrangian is [itex]e\bar{\psi}\gamma^\mu A_\mu \psi[/itex]. Since three fields take part in the interaction, these are 3-vertices.
  7. Feb 9, 2012 #6

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    But that's what Feynman diagrams are.

    They are not little cartoons describing collisions between billiard-ball like particles. They are a calculational shorthand for terms in a Lagrangian.
  8. Feb 9, 2012 #7
    The simpler electroweak processes are all three-vertices:
    • two fermions interacting with a W boson;
    • two fermions interacting with a Z boson; or
    • two fermions or a W boson interacting with a photon.
    In general, the number of fields multiplied together in each Lagrangian term imply interactions with that number of particpants. If there are only two - in which case they will always be a field and conjugate of either the same field or its chiral partner, the term represents
    • a kinetic term, if it has one or more partial differential operators (eg [itex]\bar{\psi}\gamma^{\mu}\partial_{\mu}\psi[/itex] or [itex]F^{\mu\nu}F_{\mu\nu}[/itex]), or
    • a mass term, if not (eg [itex]m\bar{\psi}_L\psi_R[/itex]).
    ([itex]F^{\mu\nu}F_{\mu\nu}[/itex] does have differential operators but they are "hidden" in its definition ([itex]F^{\mu\nu} = \partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}[/itex])).
  9. Feb 9, 2012 #8
    Thank you! I think I have a clearer picture in my head now.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook