Question

How do we know for sure a theory is non-renormalizable?

Answer 1

In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power counting due to Weinberg? This question is already answered in a previous question.

My question result from the fact that the Yang-Mills Lagrangian was considered to be non-renormalizable, and thus non-physical, for a decade until Veltman and 't Hooft found a method to regularize the theory. Keeping this in mind, is it possible that there are theories that we today consider to be non-renormalizable, and thus non-physical, which actually are renormalizable but we haven't (yet) discovered a way to do this?

I apologize in advance if my question is vague and if I'm using the wrong terminology, but I'm very new to the idea of renormalizability.

Answer 2

Hey mate here is your answer in attachment