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Amplitude of Feynman diagram in ##\phi^4## interactions
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[QUOTE="JD_PM, post: 6484249, member: 655284"] The "trick" is to ask yourself the question "how many four-momentum terms can be fixed by energy-momentum conservation?" Note that in your particular example you have 3 vertices, where energy-momentum conservation holds. Based on your notation, from left to right we get ##p_1+p_2 = k_1 + k_2, \quad k_1 + k_2 = k_3 + k_4, \quad k_3 + k_4 = q_1 + q_2## (and do not forget ##p_1+p_2 = q_1+ q_2## due to the Dirac delta function. However, your confusion is not related directly to the Dirac delta so let's focus on the vertices instead). You have ##4## internal momentum terms. The question is: how many of those can you rewrite in terms of others via energy-momentum conservation? With the above equations you can see the answer is two and the and the term associated to the diagram reads (I chose to leave ##k_2## and ##k_4## as the independent ones) \begin{equation*} 2\pi ^4 \delta^{(4)} (q_1+q_2- p_1 -p_2) \frac{(-i \lambda)^3}{4} \int {\frac{d^4 k_2 d^4 k_4}{(2\pi)^8}} \frac{i}{k_2^2 -m^2 +i\epsilon} \frac{i}{k_4^2 -m^2 +i\epsilon} \times \\ \frac{i}{(p_1 +p_2 - k_2)^2 -m^2 +i\epsilon} \frac{i}{(p_1 +p_2 - k_4)^2 -m^2 +i\epsilon} \end{equation*} PS: If you are not acquainted with asking yourself how many momentum terms are fixed, I recommend you study the Feynman rules of QED and in particular the rule that deals with such question. For instance, you can find it in Mandl & Shaw, section 7.3 (the rule of your interest is 7.). [/QUOTE]
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Amplitude of Feynman diagram in ##\phi^4## interactions
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