# Why are dimension > 4 operators non-renormalizable?

#### fliptomato

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

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#### vanesch

Staff Emeritus
Gold Member
fliptomato said:
(I guess somehow the renormalization group flow for such coupling constants diverges a mass scale given by the coupling?)
It is exactly that ! It is explained for example in Ch 12 of Peskin and Schroeder, although quite sketchy.

cheers,
Patrick.

#### Hans de Vries

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

cheers,
Patrick.
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:

Regards, Hans.

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