Divergence of the amplitude for a Feynman diagram

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SUMMARY

The forum discussion centers on the divergence of the amplitude in a specific Feynman diagram as presented in Voja Radovanovic's "Problem Book Quantum Field Theory." Participants analyze the mathematical intricacies of the integrals involved, questioning why certain terms remain finite while others diverge. The conversation emphasizes the need for clarity regarding the physical implications of these results, particularly in the context of quantum field theory calculations.

PREREQUISITES
  • Understanding of Feynman diagrams and their role in quantum field theory.
  • Familiarity with integral calculus and its application in physics.
  • Knowledge of quantum field theory concepts, particularly amplitude calculations.
  • Experience with divergence and convergence in mathematical physics.
NEXT STEPS
  • Study the mathematical foundations of Feynman diagrams in quantum field theory.
  • Learn about regularization techniques to handle divergent integrals.
  • Explore the physical significance of amplitudes in particle interactions.
  • Investigate specific examples of divergent integrals in quantum field theory.
USEFUL FOR

Physicists, graduate students in theoretical physics, and anyone studying quantum field theory who seeks to deepen their understanding of amplitude calculations and their implications.

Raymont
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1. The problem statement
In calculating the amplitude for the diagram[1], view 1.jpg.
[1] Voja Radovanovic, Problem Book Quantum Field Theory

2. Homework Equations

View 2.jpg.

The Attempt at a Solution


View 3.jpg.[/B]
Why the integrals is divergent? Why the other terms are finite?
 

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The physical significance of the results are not very clear, can anyone explain it?
 

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