How to explain the smallness of mass while the mass parameter diverge rapidly in ?

[ndung200790]

Please teach me this:
How to understand the smallness of mass while the mass parameter diverge rapidly in renormalization group flow because the mass term in Lagrangian is the relevant operator.By the way,are there always exist the fix point of renormalization group flow in any QTF Theory,or in some theory this point does not exist?
Thank you very much for any instruction.

 

[ndung200790]

This problem happen e.g in Phi4 Theory.

 

[Polyrhythmic]

The divergent mass term in the Lagrangian is nothing that you can actually measure physically, it just appears to cancel out divergences that arise in the perturbation series. I don't think it is proven that any quantum field theory has to posess a fixed point in the RG flow.

 

[ndung200790]

Please explain more detail,because in renormalization group procedure all thing be done after renormalization.But the mass parameter still diverge rapidly in renormalization group flow.

 

[ndung200790]

I do not know whether the evolutional mass flow is before or after renormalization,but if it is before renormalization then what is the meaning of renormalization group?

 

[ndung200790]

Thank Mr Polyrhythmic very much! Now I have just understood that the renormalization group is fulfiled ''before'' the renormalization to distroy the infinities.Then after renormalization group flow being done,there are still exist the infinities(the divergence of mass parameter).

 

[ndung200790]

At the moment,I think that the renormalization group flow is fulfiled ''after'' the renormalization that having accounted the UV cutting-off(in loop integrals),because we know that the Callan-Symanzik functions are independent of the momentum UV cutting-off(in loop integrals).Then the meaning of renormalization group flow is it permits us to know about the physics at any scale of space-time distance(the scale depends on the renormalization conditions).Is that correct?

 

[Polyrhythmic]

At the moment,I think that the renormalization group flow is fulfiled ''after'' the renormalization that having accounted the UV cutting-off(in loop integrals),because we know that the Callan-Symanzik functions are independent of the momentum UV cutting-off(in loop integrals).Then the meaning of renormalization group flow is it permits us to know about the physics at any scale of space-time distance(the scale depends on the renormalization conditions).Is that correct?

That sounds correct.