1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why are dimension > 4 operators non-renormalizable?

  1. Jun 22, 2005 #1
    Hi everyone--I'm curious why terms in the Lagrangian with mass dimension greater than four are "nonrenormalizable."

    I understand that the action must be dimensionless, hence the Lagrangian [density] has mass dimension 4. However, in effective field theories, we can end up with terms of dimension > 4, hence the coupling must have negative dimension. What's so bad about this?

    (I guess somehow the renormalization group flow for such coupling constants diverges a mass scale given by the coupling?)

    Thanks,
    Flip
     
  2. jcsd
  3. Jun 22, 2005 #2

    vanesch

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It is exactly that ! It is explained for example in Ch 12 of Peskin and Schroeder, although quite sketchy.

    cheers,
    Patrick.
     
  4. Jun 22, 2005 #3

    Hans de Vries

    User Avatar
    Science Advisor

    Peskin and Schroeder first talks about this in chapter 4 after introducing
    the φ4, QED and Yukawa interaction terms, See bottom of page 79.

    Then there's more in chapter 10.

    PS: Thanks to Google-Print we may hope to link directly to the appropriate
    book pages like in this example here:

    Renormalizable higher order interaction terms

    Regards, Hans.
     
    Last edited: Jun 22, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?