Compton Scattering | Klein-Nishina Formula Derivation | QED | Quantum Field Theory

In this video, I show you how to derive the Klein-Nishina formula for Compton scattering. I also derive the unpolarized cross section, and the total cross section. Beyond this, I take the low energy limits of all of these things to obtain the Thompson differential scattering cross section (polarized and unpolarized) and the Thompson total scattering cross section.
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[@thephysicistcuber175]

At around 7:29 the calculation seems to have been done in the center if mass frame, in particular the square root in the energy delta function has a k_f, rather than a p_f. Which also affects the rest of the computation.

[@Hofffy]

Hello, first good video. I have some questions if you could answer me: 1. In 16:44 when you square both sides, did you use that p_i^2+k_f^2=p_f^2+k_i^2 or another? because im not sure about that 2. In 23:20 when you mention the initial electron rest frame, you mean that because the electron will have only the mass term and photon the momentum you can simplify? 3. In 24:13 what expressions you use to simplify the scattering cross section dependent of p_i,k_i,p_f,k_f,E_kf to the next expression with k_0 and k_0'? 4. In 27:19 what four momentum conservation use? i mean,i understand for E_f, but for k_0 you dont use that p_ix+k_ix=p_fx+k_fx for x,y or z component, what do you do?. Thanks (and sorry for my english )

[@RadioPhy]

thank you. good job!

[@frankkoslowski6917]

Have you tried finding symbolic solutions as shown by means of using the Python SymPy module? If nothing else it would prove excellent code integrity of the module in its capacity to handle symbolic solutions to complex problems, given that intriguing solver-function issues were encountered when tackling double-jointed 3D Penulum simulations. 😓

[@ella9966]

Hello, could you share this structurized pdf please?

[@ibrahimnehmedov5384]

It was a Little late but you can find cross section calculation in the Matthew Shwartz Quantum Field Theory and Standard Model and For more Detailed Calculations you can use Reinhard Greiner Quantum Electordynamics