Graduate QED vs Scalar QED: Proving Divergence in P&S 10.1

Click For Summary
SUMMARY

The discussion focuses on proving the convergence or vanishing of superficially divergent diagrams in Peskin and Schroeder's Problem 10.1, specifically for 1-photon, 3-photon, and 4-photon vertex diagrams in Quantum Electrodynamics (QED) and Scalar QED. It emphasizes the use of charge-conjugation invariance for odd-numbered external photon lines and the application of the Ward-Takahashi identity for the four-photon vertex to demonstrate finiteness at any loop order. The necessity of combining all diagrams at a given order before integrating is highlighted as a crucial step in the proof.

PREREQUISITES
  • Understanding of Quantum Electrodynamics (QED)
  • Familiarity with Scalar QED concepts
  • Knowledge of charge-conjugation invariance
  • Proficiency in applying the Ward-Takahashi identity
NEXT STEPS
  • Study the implications of charge-conjugation invariance in QED
  • Research the Ward-Takahashi identity and its applications in quantum field theory
  • Explore the concept of superficially divergent diagrams in quantum electrodynamics
  • Examine the process of combining diagrams before integration in perturbative calculations
USEFUL FOR

The discussion is beneficial for theoretical physicists, graduate students in quantum field theory, and anyone studying the intricacies of gauge invariance and divergence in QED and Scalar QED.

Higgsy
Messages
18
Reaction score
0
In Peskin and Schroeder problem 10.1 is about showing that superficially divergent diagrams that would destroy gauge invariance converge or vanish. We are supposed to prove it for the 1-photon, 3-photon, and 4-photon vertex diagrams. Does this change for scalar QED?
 
Physics news on Phys.org
If this is a homework question, please post it in the homework forum.

Some hints: To show that proper verices with an odd number of external photon lines only, use the charge-conjugation invariance of QED, which holds for both spinor and scalar QED. For the four-photon vertex, use the corresponding Ward-Takahashi identity to show that it is finite at any loop order. Note that you have to combine all diagrams at a given order before you to the integrals to make this explicit for concrete examples of diagrams!
 

Similar threads

Why Is the Photon One-Point Function Zero in QED?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Derivation of the Yang-Mills 3 gauge boson vertex
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad QED replacing photon field with current in 3-point function
  • · Replies 1 ·
Replies
1
Views
1K
Graduate How the g factor comes from QFT?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Does Dim Reg really avoid a photon mass?
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Uncovering the Combinatorial Origins of Yang-Mills Theory?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Progress In Calculating The HLbL Contribution To Muon g-2
  • · Replies 0 ·
Replies
0
Views
2K
Gauge invariance/Lorentz invariance of regulator in QED
  • · Replies 7 ·
Replies
7
Views
4K
Calculating Divergent Amplitude in Phi-4 Theory
  • · Replies 1 ·
Replies
1
Views
2K
This integration appeared in the reconstruction of cross section
  • · Replies 15 ·
Replies
15
Views
3K