Why we must demonstrate the electroweak theory to be renormalizable?

In summary, Thooft showed that electroweak theory could be renormalizable if the coupling constant was dimensionless.
  • #1
ndung200790
519
0
In general speaking,if the coupling constant is (mass) dimensionless then the quantum field theory is renormalizable.In electroweak theory the coupling constant g~e,so the coupling constant is dimensionless,then the electroweak theory(Weinberg-Salam theory) would be renormalizable.So I do not understand why in 1971(I have heard that) t' Hooft must demonstrate the Weinberg-Salam to be renormalizable.I also can not find in any textbook the t'Hooft's demonstration,where can I find it?
Please forgive me if my question is not good question(I have to self-study the subject)
 
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  • #2
I have known that in electroweak theory we have to solve the anomaly problem.But I do not understand why the anomaly problem relates with the renormalization problem(divergent problem)
 
  • #3
In general proving that a theory is renormalizable is not an easy task. First you must make sure that any divergent integrals can be absorbed by a finite set of counter terms, you must properly fix the gauge while at the same time making sure that any non-physical degrees of freedom do not appear in physical calculations.

I do not quite remember what Thooft did but I do know one of his contributions was dimensional regularization which brought leaps and bounds on our abilities to do regularization in a Lorentz covariant way.
 
  • #4
Thank jarod very much!
 
  • #5
The dimensional analysis gives you a hint on the structure of counter terms; it doesn't say anything regarding quantization anomalies which could arise in loop calculations. So one major step was to provide a regularization method which preserves the "physical anomaly structure" (triangle anomalies in chiral theories) and to study their cancellation w/o introducing "unphysical anomalies" which would arise e.g. in the unmodified Pauli–Villars regularization approach.
 
  • #6
We do not need it to be renormalizable but we need it to be stable. That y we made it renormalizable.
 
  • #7
So,is there any relation between anomalies and renormalization characteristic?
 
  • #8
It seems that there is a close relation between Ward(Taylor) Identity and BPHZ theorem?
 

1. What is the Electroweak Theory?

The Electroweak Theory is a scientific theory that describes the unification of the electromagnetic and weak nuclear forces, two of the four fundamental forces of nature. It explains how these two forces are related and how they interact with matter.

2. Why is it important to demonstrate the Electroweak Theory to be renormalizable?

Demonstrating that the Electroweak Theory is renormalizable is crucial because it ensures that the theory is mathematically consistent and can be used to make accurate predictions about the behavior of particles and their interactions. A renormalizable theory also allows for the incorporation of quantum corrections, which are essential for understanding the behavior of particles at a fundamental level.

3. How is the renormalizability of the Electroweak Theory tested?

The renormalizability of the Electroweak Theory is tested through a process called perturbation theory. This involves calculating the probability of different particle interactions and comparing them to experimental data. If the calculated probabilities match the experimental results, it indicates that the theory is renormalizable.

4. What are the implications if the Electroweak Theory is not renormalizable?

If the Electroweak Theory is not renormalizable, it would mean that the theory is incomplete and cannot fully explain the behavior of particles and their interactions. It would also suggest that there may be other, unknown fundamental forces at play, which would have significant implications for our understanding of the universe.

5. Has the renormalizability of the Electroweak Theory been confirmed?

Yes, the renormalizability of the Electroweak Theory has been confirmed through numerous experiments, including the discovery of the Higgs boson in 2012. This discovery provided strong evidence for the validity of the theory and its ability to accurately describe the behavior of particles and their interactions.

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