Concept of a renormalizable theory in Weinberg's feild theory book

In summary, the concept of a renormalizable theory in Weinberg's field theory book involves removing infinities by adding all possible interactions allowed by gauge and Lorentz symmetry to the Lagrangian. However, in a renormalizable theory, there are no nonrenormalizable interactions. It is suggested to read other sources such as Srednicki or A. Zee's "QFT in a nutshell" for a better understanding of renormalization. Another recommended textbook is Collins' "Renormalization," although it is best to have prior knowledge of other basics of QFT before reading it.
  • #1
nughret
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I have just started to study the concept of a renormalizable theory in Weinberg's field theory book. I am not sure if my understanding of the process is correct and would like some additional explanation or corrections; As far as I understand in any theory there will be unrenormalizable interactions, however these infinities will be removed if we add all possible interactions allowed by gauge and lorentz symmetry to the lagrangian. I firstly don't understand how this process exactly works.
Secondly it appears to me that it is then claimed that even in an unrenormalizable theory such a lagrangian will lead to finite interaction terms and this part i really don't get, but i am not sure if i have just misunderstood this.
Any help would be greatly appreciated.
 
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  • #2


nughret said:
As far as I understand in any theory there will be unrenormalizable interactions

No, in a renormalizable theory, there are no nonrenormalizable interactions.

Weinberg is not the best place to start. I suggest Srednicki.
 
  • #3


Weinberg is probably referring to dimension >4 terms that generically do appear (they are consistent with gauge and lorentz invariance). These of course are nonrenormalizable, though heavily suppressed by some large mass scale and so can be safely integrated out in an effective theory.
 
  • #4


Avodyne said:
Weinberg is not the best place to start. I suggest Srednicki.
I agree. Personally, I suggest A. Zee, "QFT in a nutshell".
 
  • #5


Thanks I will have a look into these books, i was wondering though if anyone had a source that was aimed at renormalization specifically rather than the entire basics of field theory
 
  • #6


nughret said:
Thanks I will have a look into these books, i was wondering though if anyone had a source that was aimed at renormalization specifically rather than the entire basics of field theory
There is such a textbook: Collins "Renormalization".
But it makes sense to read it only if you are already familiar with other basics of QFT.
 

Related to Concept of a renormalizable theory in Weinberg's feild theory book

1. What is the concept of a renormalizable theory?

The concept of a renormalizable theory refers to a quantum field theory that can be mathematically adjusted to eliminate divergences, or infinities, that arise in the calculations. This process is known as renormalization and allows for the theory to make meaningful predictions.

2. Why is renormalizability important in Weinberg's field theory book?

Renormalizability is important in Weinberg's field theory book because it allows for the theory to make accurate predictions about the behavior of particles and interactions. Without renormalizability, the theory would be plagued by infinities and would not be able to make meaningful predictions.

3. How does renormalizability affect the validity of a theory?

A renormalizable theory is considered to be more valid because it can produce finite and meaningful results. This means that the theory can be used to accurately describe and predict physical phenomena, making it a more reliable and accepted theory in the scientific community.

4. Can non-renormalizable theories still be useful?

Yes, non-renormalizable theories can still be useful in certain contexts. They may be able to make predictions in certain energy regimes or be used as a starting point for developing more complete theories. However, they are not considered to be as fundamental or reliable as renormalizable theories.

5. How do we determine if a theory is renormalizable?

A theory is considered renormalizable if it can be mathematically adjusted to eliminate infinities through the process of renormalization. This is typically determined through extensive calculations and testing of the theory's predictions. If the theory consistently produces finite and accurate results, it is considered to be renormalizable.

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