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Differences between rnormalizable and nonrenormalizable... 
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#1
Jan1404, 01:26 PM

P: 215

I would like to know the differences between a renormalizable and Nonrenormalizable theory..how is possible that one gives finite results and the other infinite results?..why happens that?..in fact i supose that the divergences in both theories go as
Int(0,Infinite)d^npp^n then why in one thoery can be absorved wheres in the other not?... 


#2
Jan1404, 02:30 PM

P: 16

There are infinities in both types of theoreis. However, there is a finite number of them in renormalizable theories and infinite number  in nonrenormalizable. The trick with predictions here works because in renormalizable theories you can redefine some of your basic parameters (mass, charge, etc.) to absorb those divergencies. This procedure of redefinition is fine, since the integrals that come out divergent in perturbation theory are divergent in the ultraviolet, i.e. probe very short distances at which you don't know anything about real physics anyway. So one redefines those parameters and extracts their values from experiment...
BTW, nonrenormalizable theories are not waste either. There is a number of welldefined NR theories  effective field theories  such as chiral perturbation theory, heavy quark effective theory or even gravity in postnewtonial limit  which produce a wealth of very useful predictions. They just have more parameters to fit order by order in small parameter expansion... 


#3
Jan2204, 03:11 PM

P: 215

I rode in peskinschroeder book a thing but i do not know if has to deal with renormalization, they saisd that green function at all orders could be calculated because it solved a differential equation so you could solve it to get the green function to all orders.....sorry if i am wrong but could it be applied to nonrenormalizable theories to get the green functions?..by the way knowing the green function allows you to solve the renormalization problem?...thanks.
P.D :i am ignorant in this matter could someone provide a link to a good introduction (math included) to renormalization?..thnx.. 


#4
Jan2304, 11:08 AM

PF Gold
P: 2,893

Differences between rnormalizable and nonrenormalizable...
If you style pickingup small random papers as a learning method, check the ones at http://web.mit.edu/redingtn/www/netadv/Xrenormali.html
If you prefer a book path, the Peskin is a good option, but you could want to try, before, the 3volume, out of print, series from Bjorken Drell, as the PeskinShroeder builds upon it. Last, any new (post1990) book using the Roperation of bogoliugov must do the finishing touch. 


#5
Jan2304, 11:18 AM

PF Gold
P: 2,893

On other hand, let me to provide a fast introduction to renormalization.
Take a function f(x). The quantity f(x)/x is clearly infinite at 0. But if you substract the infinite f(0)/x, you will get a finite quantity which we call f'(0) 


#6
Jan2304, 01:14 PM

Sci Advisor
P: 660




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