How can we solve IR divergences problem?

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Discussion Overview

The discussion revolves around the problem of infrared (IR) divergences in quantum field theory (QFT), particularly in the context of quantum electrodynamics (QED) and quantum chromodynamics (QCD). Participants explore various methods for addressing these divergences, including regularization techniques and the treatment of mass singularities.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to solve IR divergence problems, noting that UV divergences are addressed through renormalization.
  • Another participant suggests that IR divergences can also be handled through regularization and imposing a cutoff, similar to UV divergences, and shares resources for further reading.
  • A different participant mentions that in QED, the standard approach involves summing the cross section over configurations with soft photons and redefining asymptotic electron states to account for soft photon clouds.
  • One participant raises concerns about mass singularities in QCD, specifically referencing a section in Peskin & Schroeder regarding parton evolution and questioning the implications of non-canceling singularities.
  • A later reply questions the differences between singularities arising from the limit as momentum approaches zero when mass is zero versus those arising from momentum squared approaching mass squared.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to IR divergences, with no consensus on a single method or resolution of the issues raised. The discussion remains unresolved regarding the implications of mass singularities in QCD.

Contextual Notes

Participants reference specific textbooks and papers, indicating a reliance on particular definitions and frameworks that may not be universally accepted. The discussion highlights the complexity of the topic and the need for further clarification on certain mathematical aspects.

ndung200790
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Please teach me this:
The UV divergence problems are solved by Renormalization Procedure,but I do not understand how to solve IR divergence problems.
Thank you very much for your kind helping.
 
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I am no expert in re-normalisation but my understanding is it is solved in the same way - by regularisation, imposing a cutoff, and then taking the limit:
http://www.hep.phys.soton.ac.uk/hepwww/staff/D.Ross/qft/aqft5.pdf

Right now I am going a bit deeper into QFT than I have before and this is something I too am trying to grasp. The following paper really helped me a lot by exposing its mathematical underpinnings:
http://arxiv.org/pdf/hep-th/0212049.pdf

Thanks
Bill
 
Last edited by a moderator:
ndung200790 said:
Please teach me this:
The UV divergence problems are solved by Renormalization Procedure,but I do not understand how to solve IR divergence problems.
If you're talking about QED, the usual textbook procedure is to sum the cross section over all possible configurations with soft photons in the final state. See, e.g., Peskin & Schroeder.

Another approach is to redefine the asymptotic electron states to include soft photon clouds.

BTW, which textbook(s) are you studying from?
 
I am studying Peskin&Schroeder and I am confused with mass singularities in QCD(Parton evolution).
 
In Peskin&Schroeder (&17.5 Parton Evolution)saying ''...when quarks and gluons appear in initial state of parton subprocess,...mass singularities do not cancel''.Then I worry if there are any disasters because of the singularities?
 
And are there any differences between the singularities because of p→0 when m=0 and the singularities because of p[itex]^{2}[/itex]→m[itex]^{2}[/itex]?
 

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