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

 

[vanesch]

(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]

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

cheers,
Patrick.

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

Regards, Hans.