Differences between rnormalizable and non-renormalizable

  • Thread starter eljose79
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In summary: Ward identities are a consequence of the renormalization group. They allow you to calculate the Green functions from first principles.
  • #1
eljose79
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-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 theory can be absorved wheres in the other not?...
 
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  • #2
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...
 
  • #3
-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..
 
  • #4
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.
 
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  • #5
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)
 
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  • #6
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?
 

1. What is the meaning of "normalizable" and "non-renormalizable" in relation to physics?

The terms "normalizable" and "non-renormalizable" refer to the mathematical properties of an equation or theory in physics. A normalizable theory is one in which the calculations and results can be made finite, or well-defined, through a process called renormalization. A non-renormalizable theory, on the other hand, is one in which the calculations and results cannot be made finite through renormalization.

2. How does renormalization work in normalizable theories?

In normalizable theories, the process of renormalization involves adjusting certain parameters in the equations to account for interactions between particles. This allows for the elimination of infinite or undefined quantities, making the theory mathematically consistent and predictive.

3. What are some examples of normalizable and non-renormalizable theories?

Examples of normalizable theories include quantum electrodynamics (QED) and the standard model of particle physics. These theories have been successfully used to make accurate predictions in experiments. Non-renormalizable theories include theories of quantum gravity and some versions of string theory, which have not yet been experimentally confirmed due to their infinite or undefined predictions.

4. What are the implications of a theory being non-renormalizable?

A non-renormalizable theory does not necessarily mean that it is incorrect or unusable. However, it does indicate that the theory is incomplete and may not accurately describe the physical world at all energy scales. This can limit its usefulness and applicability in certain situations.

5. Can a non-renormalizable theory ever be made into a normalizable one?

It is possible for a non-renormalizable theory to be modified or extended in a way that makes it normalizable. This is often referred to as "taming" the theory. However, this process can be complex and may require significant changes to the original theory, making it less elegant and less predictive. As of now, there is no universally accepted method for taming non-renormalizable theories.

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