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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?)

  2. jcsd
  3. Jun 22, 2005 #2


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

  4. Jun 22, 2005 #3

    Hans de Vries

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    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:

    http://print.google.com/print?id=ZbTXdWsrsAEC&lpg=237&dq=renormalizable+higher+order+interaction+term&prev=http://print.google.com/print%3Fie%3DUTF-8%26q%3Drenormalizable%2Bhigher%2Border%2Binteraction%2Bterm%26btnG%3DSearch&pg=237&sig=5Vrhek6UvWRHsdqimJlTP0ACCrY [Broken]

    Regards, Hans.
    Last edited by a moderator: May 2, 2017
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