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

In summary: The renormalization group flow is a procedure used to account for infinities in quantum field theories, particularly in the mass term. It is done before the actual renormalization process and allows us to understand the physics at any scale based on the chosen renormalization conditions. It is not proven that all quantum field theories have a fixed point in the renormalization group flow.
  • #1
ndung200790
519
0
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.
 
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  • #2


This problem happen e.g in Phi4 Theory.
 
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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.
 
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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.
 
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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?
 
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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).
 
  • #7


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?
 
  • #8


ndung200790 said:
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.
 

1. How does the smallness of mass relate to the rapid divergence of the mass parameter?

The smallness of mass and the rapid divergence of the mass parameter are two different concepts that are often confused. The smallness of mass refers to the actual value of mass, while the rapid divergence of the mass parameter refers to the behavior of the mass parameter in certain mathematical equations. Therefore, they are not directly related to each other.

2. What causes the rapid divergence of the mass parameter?

The rapid divergence of the mass parameter is a result of certain mathematical equations used in theoretical physics. These equations involve the concept of renormalization, which is used to remove infinities and make the equations more manageable. However, this process can lead to the mass parameter diverging rapidly.

3. Can the smallness of mass be explained by the Higgs mechanism?

The Higgs mechanism is a theory that explains how particles acquire mass. However, it does not directly explain the smallness of mass. The Higgs mechanism allows for the existence of particles with different masses, but it does not determine the actual value of their masses.

4. How do physicists deal with the rapid divergence of the mass parameter in their calculations?

Physicists use various techniques, such as renormalization, to deal with the rapid divergence of the mass parameter in their calculations. These techniques help to remove the infinities and make the equations more meaningful and accurate.

5. Is there a theoretical explanation for the smallness of mass?

There is currently no definitive theoretical explanation for the smallness of mass. The Standard Model of particle physics, which is the most successful theory to date, does not provide an explanation for the smallness of mass. This is still an active area of research in theoretical physics.

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