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

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Discussion Overview

The discussion revolves around understanding the smallness of mass in the context of renormalization group (RG) flow, particularly in quantum field theories (QFT) such as Phi4 Theory. Participants explore the implications of mass divergence in the Lagrangian and the existence of fixed points in RG flow.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to understand how mass can be small while the mass parameter diverges rapidly in RG flow, questioning the nature of the mass term as a relevant operator in the Lagrangian.
  • Another participant notes that the divergent mass term is not physically measurable and serves to cancel divergences in the perturbation series, raising doubts about the necessity of fixed points in RG flow for all QFTs.
  • There is a request for clarification on the timing of mass flow in relation to renormalization, with one participant suggesting that the RG flow occurs after renormalization, while another believes it happens before.
  • One participant expresses understanding that RG flow is conducted before renormalization to address infinities, yet acknowledges that divergences in the mass parameter persist.
  • Another participant asserts that RG flow allows for insights into physics at various scales, contingent on renormalization conditions, and seeks confirmation of this interpretation.

Areas of Agreement / Disagreement

Participants express differing views on the timing of RG flow relative to renormalization and the implications of mass divergence. There is no consensus on whether fixed points must exist in all QFTs, and the discussion remains unresolved regarding the nature of mass flow.

Contextual Notes

There are unresolved questions regarding the assumptions about the relationship between renormalization and RG flow, as well as the implications of mass divergence in the context of physical measurements.

ndung200790
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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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This problem happen e.g in Phi4 Theory.
 


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.
 


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.
 


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?
 


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).
 


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?
 


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.
 

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