Help me in QTF theory(t'Hoof's method)?

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SUMMARY

The discussion centers on the application of dimensional regularization using t'Hoof's method to address the infinite mass of photons and the violation of the Ward identity. Specifically, it examines the one-loop self-energy of photons as detailed in Chapter 7.5 of Schroder and Peskin's "Quantum Field Theory" (QFT). The key conclusion is that reducing the dimensionality of loop integrals from four to two transforms the order of divergence from quadratic to logarithmic, a phenomenon that may initially seem counterintuitive but is clarified in section 10.1.2 of Mandl and Shaw's QFT book.

PREREQUISITES
  • Understanding of dimensional regularization in quantum field theory
  • Familiarity with the Ward identity and its implications
  • Knowledge of one-loop self-energy calculations
  • Proficiency in the concepts presented in Schroder and Peskin's QFT
NEXT STEPS
  • Study the details of dimensional regularization in t'Hoof's method
  • Review the derivation of the Ward identity and its significance in QFT
  • Examine one-loop self-energy calculations in various quantum field theories
  • Read section 10.1.2 of Mandl and Shaw's QFT for further insights
USEFUL FOR

This discussion is beneficial for theoretical physicists, quantum field theorists, and advanced students seeking to deepen their understanding of dimensional regularization and its applications in quantum field theory.

ndung200790
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Please help me this problem:
Considering dimensional regularization(t'Hoof method) to solve the infinite mass of photon and so that the violation of Ward identity problem,we restrict to consider one loop self energy of photon aproximation(in Schroder and Peskin's QTF book,7.5 chapter 7).I don't understand why reducing the 4 space-time dimensions to 2 dimensions( the dims of loop integral) then the order of divergence reduce from quadratic divergence(at 4 dims) to logarithmic divergence(at 2 dims).Because it seem to me by decreasing 1 dimension of integral,the divergence decreases by 1 order in power,so it would not be logarithmic divergence at 2 dimensions integral.
Thank you very much in advanced.
 
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I have just found out the answer in 10.1.2 in QTF book of Mandl&Shaw
 

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