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

  • Context: Graduate 
  • Thread starter Thread starter nughret
  • Start date Start date
  • Tags Tags
    Book Concept Theory
Click For Summary

Discussion Overview

The discussion revolves around the concept of renormalizable theories as presented in Weinberg's field theory book. Participants explore the nature of renormalizable versus unrenormalizable interactions, the implications of adding interactions to the Lagrangian, and seek additional resources for understanding renormalization specifically.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses uncertainty about the process of renormalization and the role of unrenormalizable interactions in theories.
  • Another participant asserts that in a renormalizable theory, there are no nonrenormalizable interactions, challenging the initial claim.
  • A different viewpoint suggests that Weinberg may refer to higher-dimensional terms that are nonrenormalizable but can be integrated out in an effective theory due to being suppressed by a large mass scale.
  • Several participants recommend alternative textbooks, such as Srednicki and A. Zee's "QFT in a Nutshell," as potentially better starting points for understanding the topic.
  • One participant seeks a source specifically focused on renormalization rather than general field theory, leading to a suggestion of Collins' "Renormalization," with a note on the prerequisite knowledge needed.

Areas of Agreement / Disagreement

Participants express differing views on the nature of unrenormalizable interactions in theories, indicating a lack of consensus on the initial claims about renormalization. Recommendations for alternative resources also vary among participants.

Contextual Notes

There are unresolved assumptions regarding the definitions of renormalizable and unrenormalizable interactions, as well as the implications of adding interactions to the Lagrangian. The discussion reflects varying levels of familiarity with the subject matter among participants.

Who May Find This Useful

This discussion may be useful for students and researchers interested in quantum field theory, particularly those looking to understand the nuances of renormalization and seeking appropriate resources for study.

nughret
Messages
45
Reaction score
0
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.
 
Physics news on Phys.org


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.
 


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.
 


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


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
 


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.
 

Similar threads

Graduate QED Bound States: Weinberg's Explanation & Breakdown
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Renormalizability conditions for a real scalar field in d dimensions
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Is renormalization the ideal solution?
  • · Replies 57 ·
2
Replies
57
Views
8K
Graduate Coupling constants with fractional dimensions
  • · Replies 2 ·
Replies
2
Views
2K
Graduate I have some naive questions about the Reeh-Schlieder theorem
  • · Replies 1 ·
Replies
1
Views
2K
Books on Weak Interaction
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad QED replacing photon field with current in 3-point function
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Exact symmetry, quantum states, and symmetric dynamics
  • · Replies 8 ·
Replies
8
Views
1K
Graduate Structure of Matter in Quantum Field Theory
  • · Replies 75 ·
3
Replies
75
Views
10K
Graduate A query on the (old) motivation for renormalizable theories
  • · Replies 5 ·
Replies
5
Views
3K