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I'm a self-studying 14-year-old who has a passion for particle physics. I'm currently trying to calculate the QED photon propagator to one loop. However, in all the places I've looked, even with the same renormalization scheme, the results are different. I don't get it. Also, I need a step-by-step tutorial on how to calculate that trace in the numerator, specifically, the one with those gamma matrices.

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We can't really answer this unless you give some more details. Even though this isn't a homework question, I recommend you follow some of the advice in our homework policy in formulating your question: what have you tried? Where do you get stuck? The more detail you include in the question (to a point), the more useful help you can get. –  David Z May 5 '13 at 19:26
    
First read this article on Gamma matrices, especially the part of the article about product and traces of gamma matrices. –  Trimok May 6 '13 at 7:52
    
And when you say that you see different results with the same renormalization scheme, give references to prove your assertion. –  Trimok May 6 '13 at 8:01
    
Well, the product and trace rules only apply if they're in a specific order. They're not in the right order here. –  Darius Goad May 6 '13 at 13:46
    
W. Greiner's QED often has step by step procedure, although i don't like that book so much.. –  user26143 Aug 4 '13 at 10:43
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1 Answer

This link has a very easy to follow derivation of the scalar field Feynman propagator. Once you understand that, you should be able to do it for vector particles like photons too. The correct answer is given at the end of the chart in this link.

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That's not it. I need a calculation of the photon self-energy to one loop order. –  Darius Goad May 5 '13 at 21:42
    
Well that's not really what you asked for. How about this: 152.78.192.50/hepwww/staff/D.Ross/qft/aqft3.pdf ? –  elfmotat May 5 '13 at 22:00
    
Yes it was. Also, I tried that one. –  Darius Goad May 6 '13 at 1:17
    
Dear @elfmotat: It is best to supply titles, authors, etc, of links, so we can reconstruct the links in case of future link rot. –  Qmechanic Jun 4 '13 at 21:53
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