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Differences between rnormalizable and non-renormalizable...

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eljose79
#1
Jan14-04, 01:26 PM
P: 215
-I would like to know the differences between a renormalizable and Non-renormalizable 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?...
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Yustas
#2
Jan14-04, 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 well-defined NR theories -- effective field theories -- such as chiral perturbation theory, heavy quark effective theory or even gravity in post-newtonial limit -- which produce a wealth of very useful predictions. They just have more parameters to fit order by order in small parameter expansion...
eljose79
#3
Jan22-04, 03:11 PM
P: 215
-I rode in peskin-schroeder 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 non-renormalizable 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..

arivero
#4
Jan23-04, 11:08 AM
PF Gold
arivero's Avatar
P: 2,907
Differences between rnormalizable and non-renormalizable...

If you style picking-up 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 3-volume, out of print, series from Bjorken Drell, as the Peskin-Shroeder builds upon it.

Last, any new (post-1990) book using the R-operation of bogoliugov must do the finishing touch.
arivero
#5
Jan23-04, 11:18 AM
PF Gold
arivero's Avatar
P: 2,907
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)
jeff
#6
Jan23-04, 01:14 PM
Sci Advisor
P: 660
Originally posted by eljose79 ...i do not know if has to deal with renormalization...green function at all orders could be calculated because it solved a differential equation...but could it be applied to non-renormalizable theories...
Are you referring to ward identities?


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