# Why we must demonstrate the electroweak theory to be renormalizable?

• ndung200790
In summary, Thooft showed that electroweak theory could be renormalizable if the coupling constant was dimensionless.f

#### ndung200790

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)

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)

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.

Thank jarod very much!

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.

We do not need it to be renormalizable but we need it to be stable. That y we made it renormalizable.

So,is there any relation between anomalies and renormalization characteristic?

It seems that there is a close relation between Ward(Taylor) Identity and BPHZ theorem?