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

In summary, Peskin and Schroeder problem 10.1 deals with proving the convergence or vanishing of superficially divergent diagrams that would destroy gauge invariance. This needs to be demonstrated for the 1-photon, 3-photon, and 4-photon vertex diagrams. However, the approach may change for scalar QED, and in such cases, the charge-conjugation invariance of QED can be utilized for proper vertices with an odd number of external photon lines. Additionally, for the four-photon vertex, the corresponding Ward-Takahashi identity can be used to show its finiteness at any loop order. It is important to combine all diagrams at a given order before integrating to make this explicit
  • #1
Higgsy
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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?
 
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  • #2
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!
 

Related to QED vs Scalar QED: Proving Divergence in P&S 10.1

1. What is QED vs Scalar QED?

QED (Quantum Electrodynamics) is a theory that describes the interactions between charged particles and electromagnetic fields. Scalar QED is a simplified version of QED that only considers scalar fields, which have no direction or spin.

2. What does "Proving Divergence" mean in the context of P&S 10.1?

In P&S 10.1, "Proving Divergence" refers to showing that the mathematical equations used in QED and Scalar QED lead to different results. This is important because it demonstrates that the two theories are not equivalent.

3. How do scientists prove divergence in P&S 10.1?

Scientists prove divergence in P&S 10.1 by comparing the predictions made by QED and Scalar QED for a specific physical phenomenon. If the predictions do not match, it indicates that the two theories are not equivalent and there is a divergence between them.

4. What is the significance of proving divergence in P&S 10.1?

Proving divergence in P&S 10.1 is significant because it highlights the limitations of using simplified theories like Scalar QED. It also emphasizes the importance of considering all variables and interactions in a complex system like quantum electrodynamics.

5. How does the concept of divergence in P&S 10.1 impact our understanding of quantum physics?

The concept of divergence in P&S 10.1 challenges our understanding of quantum physics by showing that simplifications and approximations may not always be accurate. It encourages scientists to continue exploring and refining theories to better explain the complexities of the quantum world.

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