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

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SUMMARY

The discussion centers on the relationship between the Renormalization Group (RG) and the renormalizability of theories such as Quantum Electrodynamics (QED) and Gravity. It is established that if a theory is non-renormalizable, it lacks a corresponding RG equation. The existence of a continuum limit, which is determined by the presence of a UV fixed point in the RG equation, indicates that a theory is renormalizable. However, some renormalizable theories, like QED, possess infrared fixed points instead of UV fixed points, complicating the understanding of their renormalizability.

PREREQUISITES
  • Understanding of Renormalization Group (RG) equations
  • Familiarity with Quantum Electrodynamics (QED)
  • Knowledge of continuum limits in quantum field theories
  • Concept of fixed points in the context of RG analysis
NEXT STEPS
  • Study the implications of UV fixed points in quantum field theories
  • Explore the concept of continuum limits in more detail
  • Investigate the differences between infrared and ultraviolet fixed points
  • Examine the Renormalization Group approach in Gravity theories
USEFUL FOR

The discussion is beneficial for theoretical physicists, particularly those specializing in quantum field theory, as well as graduate students seeking to deepen their understanding of renormalizability and the Renormalization Group framework.

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.
 


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..
 


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.
 

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