I Compton scattering amplitude and propagator

Dhmht_Kr
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Hi everyone
How can i prove that the propagator is
1681501906264.png

And then
1681501970004.png
 

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I'm afraid answering your questions will depend on the background you'd like the explanation to be standing in. In other words, what level of QFT physics you are interested in? For instance, can I assume you're aware of how to quantize the Dirac field and then get its propagation amplitudes?

If you let me know your overall level in QFT, I might be able to answer the above questions.
 
Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'

Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'

Well, I'm simulating a neutron-proton scattering phase shift. The equation that I solve numerically is the Phase function method and is $$ \frac{d}{dr}[\delta_{i+1}] = \frac{2\mu}{\hbar^2}\frac{V(r)}{k^2}\sin(kr + \delta_i)$$ ##\delta_i## is the phase shift for triplet and singlet state, ##\mu## is the reduced mass for neutron-proton, ##k=\sqrt{2\mu E_{cm}/\hbar^2}## is the wave number and ##V(r)## is the potential of interaction like Yukawa, Wood-Saxon, Square well potential, etc. I first...
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