Does Renormalization group tell you if a theory is Renormalizable or not ?

In summary, the Renormalization group equation can determine if a theory is renormalizable or not by looking at its UV fixed point. However, there are renormalizable theories that may not have a continuum limit, such as QED, which has an infrared fixed point. The relationship between renormalizability and infrared fixed points is still unclear.
  • #1
zetafunction
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Does Renormalization group tell you if a theory is Renormalizable or not ??

the idea is this, using the Renormalization group equation for our theory (QED, Gravity, Gauge theories..) can tell this RG equation if our theory is renormalizable or not for big or small energies ??
 
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No, if the theory is non-renormalizable then by definition there is no RG equation for that theory.
 
  • #3


but you would not know if a given theory is renormalizable or not 'a priori' so perhas you could obtain a renormalization group equation or similar, for example i think there is a RG equation fro gravity..
 
  • #4


zetafunction said:
but you would not know if a given theory is renormalizable or not 'a priori' so perhas you could obtain a renormalization group equation or similar, for example i think there is a RG equation fro gravity..

The RG can tell you if the theory has a continuum limit, and that's what's being asked for gravity. For a continuum limit to exist, the RG equation must have a UV fixed point. If a continuum limit exists, then the theory is renormalizable.

However, there are renormalizable theories that don't have continuum limits, such as QED. The QED fixed point is infrared, not UV. I don't understand the relationship (if any?) between renormalizability and an infrared fixed point.
 

1. What is the purpose of the Renormalization group in theoretical physics?

The Renormalization group is a mathematical tool used in theoretical physics to study the behavior of physical systems at different scales. It helps to understand how the fundamental parameters of a theory change as we zoom in or out, allowing us to make predictions about the behavior of a system at different energy scales.

2. How does the Renormalization group determine if a theory is renormalizable?

The Renormalization group does not directly determine if a theory is renormalizable or not. However, it can provide information about the behavior of a theory at different energy scales, which can be used to determine if a theory is renormalizable. A theory is considered renormalizable if it can be made finite by a finite number of renormalization procedures.

3. Can the Renormalization group be used to prove the renormalizability of a theory?

No, the Renormalization group cannot be used to prove the renormalizability of a theory. While it can provide important insights into the behavior of a theory, the ultimate determination of renormalizability relies on mathematical proofs and experimental evidence.

4. Is a theory with a fixed point in the Renormalization group considered renormalizable?

Not necessarily. A fixed point in the Renormalization group indicates that the theory has a scale-invariant behavior, but this does not guarantee renormalizability. Other factors, such as the number of relevant couplings and the behavior of the theory at higher energy scales, must also be considered.

5. Can a non-renormalizable theory still be useful and valid?

Yes, a non-renormalizable theory can still be useful and valid in certain contexts. While it may not accurately describe all physical phenomena, it can still provide valuable insights and predictions in certain regimes. Additionally, non-renormalizable theories can serve as effective low-energy descriptions of more fundamental theories.

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