Evaluating Feynman diagram in QFT without external fermion lines

In summary, the conversation discusses the computation of the value for the diagram in Photon-Photon scattering and the issue of whether the matrix element should be a scalar or a matrix. It is suggested that the missing polarization indices for the external photon lines may be the cause of the discrepancy. It is also mentioned that for every closed fermion loop, there is a trace over the spin indices.
  • #1
Amanheis
67
0
...like in Photon-Photon-scattering. I know this doesn't make sense physically but the value for the diagram should still be computeable. If I want to put the expression for the matrix element together, I get a matrix, but it should be a scalar, right? Since the spinor bi-product is missing...
Do I have to take the trace?
 
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  • #2
I'm not quite sure what you are doing, but it sounds like you are missing the polarization indices for the external photon lines. Could that be it?
 
  • #3
No, contracting e_\mu with gamma^\mu gives still a matrix, since e_\mu is just a 4-vector. Or am I wrong on this part?
 
  • #4
For every closed fermion loop, there is a trace over the spin indices.
 
  • #5
Thanks, that helped
 

1. What is a Feynman diagram in quantum field theory (QFT)?

A Feynman diagram is a graphical representation of the interactions between particles in quantum field theory. It is used to calculate the probability of a specific scattering process or interaction between particles.

2. How do you evaluate a Feynman diagram in QFT without external fermion lines?

To evaluate a Feynman diagram without external fermion lines, you first need to assign mathematical expressions to each line and vertex in the diagram. These expressions represent the propagator for the particle and the interaction between particles, respectively. Then, you use Feynman rules to calculate the amplitude of the diagram, which is then used to determine the probability of the scattering process.

3. What are some advantages of using Feynman diagrams in QFT?

Feynman diagrams provide a visual representation of complex mathematical calculations in QFT, making it easier to understand and interpret the results. They also allow for the calculation of higher-order corrections to scattering processes, which would be difficult to do using traditional methods.

4. Can Feynman diagrams be used for all types of particle interactions?

Yes, Feynman diagrams can be used for all types of particle interactions, including electromagnetic, weak, and strong interactions. However, the specific Feynman rules for each type of interaction may vary.

5. What are some applications of evaluating Feynman diagrams in QFT?

Evaluating Feynman diagrams in QFT is essential for understanding the behavior of particles and their interactions. It is used in a wide range of applications, including particle physics experiments, particle accelerator design, and theoretical calculations of particle interactions in various physical systems.

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